Skip to content Skip to navigation

MIGSAA mini-course in harmonic analysis by Professor Arpad Benyi

x

Error message

  • Deprecated function: Return type of DatabaseStatementBase::execute($args = [], $options = []) should either be compatible with PDOStatement::execute(?array $params = null): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2244 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/maxwell/public_html/migsaa/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseCondition::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 1652 of /home/maxwell/public_html/migsaa/includes/database/query.inc).
  • Deprecated function: Optional parameter $data declared before required parameter $info is implicitly treated as a required parameter in include_once() (line 1389 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_random_bytes() (line 2268 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: Return type of DateObject::__wakeup() should either be compatible with DateTime::__wakeup(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::format($format, $force = false) should either be compatible with DateTime::format(string $format): string, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::setTimezone($tz, $force = false) should either be compatible with DateTime::setTimezone(DateTimeZone $timezone): DateTime, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/date/date_api/date_api.module).
  • Deprecated function: Optional parameter $data declared before required parameter $name is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $data declared before required parameter $name is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $file declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $account declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $entity declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $account declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $values declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $view_mode declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $langcode declared before required parameter $entity_type is implicitly treated as a required parameter in require_once() (line 341 of /home/maxwell/public_html/migsaa/includes/module.inc).
  • Deprecated function: Optional parameter $terms declared before required parameter $node is implicitly treated as a required parameter in include_once() (line 1389 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $args declared before required parameter $node is implicitly treated as a required parameter in include_once() (line 1389 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $checkbox declared before required parameter $input is implicitly treated as a required parameter in include_once() (line 1389 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: rtrim(): Passing null to parameter #1 ($string) of type string is deprecated in url() (line 2349 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: Optional parameter $base_table declared before required parameter $options is implicitly treated as a required parameter in include_once() (line 3492 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $base_field declared before required parameter $options is implicitly treated as a required parameter in include_once() (line 3492 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • Deprecated function: Return type of RulesRecursiveElementIterator::hasChildren() should either be compatible with RecursiveIterator::hasChildren(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 2088 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/rules/includes/rules.core.inc).
  • Deprecated function: Return type of RulesRecursiveElementIterator::getChildren() should either be compatible with RecursiveIterator::getChildren(): ?RecursiveIterator, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 2088 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/rules/includes/rules.core.inc).
  • Deprecated function: Return type of RulesContainerPlugin::getIterator() should either be compatible with IteratorAggregate::getIterator(): Traversable, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 2102 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/rules/includes/rules.core.inc).
  • Deprecated function: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated in url_is_external() (line 2393 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated in url_is_external() (line 2395 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: ltrim(): Passing null to parameter #1 ($string) of type string is deprecated in url() (line 2311 of /home/maxwell/public_html/migsaa/includes/common.inc).

A new MIGSAA short course in harmonic analysis is taking place 21st and 22nd April in University of Edinburgh.

Title: 'Smoothing of commutators for certain classes of bilinear operators'

When: 3 pm - 5 pm on Thursday 21st and Friday 22nd April 2016

Where: James Clerk Maxwell Building, room 6206, University of Edinburgh http://tinyurl.com/gmv9mpw

The course is given by Professor Arpad Benyi of Western Washington University whose main area of research lies at the interface of Fourier analysis, operator theory and partial differential equations.

Abstract: We will begin by reviewing, in linear setting, some basic facts about Calderon-Zygmund operators, Muckenhoupt weights and the classical result of Coifman-Rochberg-Weiss about the commutator of the Hilbert transform and BMO. We will then move on to the bilinear setting.

After stating some known facts about the corresponding objects in this theory, we will explore the smoothing effect of commutators of certain classes of bilinear operators and functions in appropriate spaces. In particular, with (p, q, r) a Holder triple, we will prove the (weighted) L^p x L^q -> L^r compactness of commutators of bilinear Calderon-Zygmund operators with functions of continuous mean oscillation as well as the L^p x L^q -> L^r boundedness of commutators of classes of bilinear pseudodifferential operators that fall outside the Calderon-Zygmund theory with Lipschitz functions.

SHARE

MIGSAA mini-course in harmonic analysis by Professor Arpad Benyi | The Maxwell Institute for Mathematical Sciences

Error

x

Error message

  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 946 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: trim(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_http_request() (line 1022 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: mb_substr(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_substr() (line 593 of /home/maxwell/public_html/migsaa/includes/unicode.inc).
  • Deprecated function: strip_tags(): Passing null to parameter #1 ($string) of type string is deprecated in syslog_watchdog() (line 114 of /home/maxwell/public_html/migsaa/modules/syslog/syslog.module).
  • Warning: Cannot modify header information - headers already sent by (output started at /home/maxwell/public_html/migsaa/includes/common.inc:2807) in drupal_send_headers() (line 1501 of /home/maxwell/public_html/migsaa/includes/bootstrap.inc).
  • TypeError: xmlsitemap_node_create_link(): Argument #1 ($node) must be of type stdClass, bool given, called in /home/maxwell/public_html/migsaa/sites/all/modules/contrib/xmlsitemap/xmlsitemap_node/xmlsitemap_node.module on line 28 in xmlsitemap_node_create_link() (line 194 of /home/maxwell/public_html/migsaa/sites/all/modules/contrib/xmlsitemap/xmlsitemap_node/xmlsitemap_node.module).
  • Deprecated function: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated in url_is_external() (line 2393 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated in url_is_external() (line 2395 of /home/maxwell/public_html/migsaa/includes/common.inc).
  • Deprecated function: ltrim(): Passing null to parameter #1 ($string) of type string is deprecated in url() (line 2311 of /home/maxwell/public_html/migsaa/includes/common.inc).
The website encountered an unexpected error. Please try again later.