Small Cap Square Function Estimates

We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) | f γ | 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We fi...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	The Journal of fourier analysis and applications 2024-06, Vol.30 (3), Article 36
1. Verfasser:	Gan, Shengwen
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Approximations and Expansions Estimates Fourier Analysis Lower bounds Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue	3
container_start_page
container_title	The Journal of fourier analysis and applications
container_volume	30
creator	Gan, Shengwen
description	We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) \| f γ \| 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We find sharp upper and lower bounds of the constant C α , p ( R ) .
doi_str_mv	10.1007/s00041-024-10095-x
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3066865178</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3066865178</sourcerecordid><originalsourceid>FETCH-LOGICAL-c200t-7d9ce92d70de2ae273256406ec40aedc405983665060be684ba66f529a2267cc3</originalsourceid><addsrcrecordid>eNp9kF9LwzAUxYMoOKdfwKfCnqM3SXPTPErZnDDwYfocsjSVja7tkhbmtzdawTdf7h8459zLj5B7Bg8MQD1GAMgZBZ7TtGtJzxdkxqRgVBaSXaYZUKcZ9TW5ifEAwJlQYkYW26Ntmqy0fbY9jTb4bDW2bth3bbaMw_5oBx9vyVVtm-jvfvucvK-Wb-Wabl6fX8qnDXUcYKCq0s5rXimoPLeeK8El5oDe5WB9larUhUCUgLDzWOQ7i1hLri3nqJwTc7KYcvvQnUYfB3PoxtCmk0YAYoGSqSKp-KRyoYsx-Nr0If0ZPg0D8w3DTDBMgmF-YJhzMonJFJO4_fDhL_of1xdgLF_8</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3066865178</pqid></control><display><type>article</type><title>Small Cap Square Function Estimates</title><source>SpringerNature Journals</source><creator>Gan, Shengwen</creator><creatorcontrib>Gan, Shengwen</creatorcontrib><description>We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) \| f γ \| 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We find sharp upper and lower bounds of the constant C α , p ( R ) .</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-024-10095-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Estimates ; Fourier Analysis ; Lower bounds ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Signal,Image and Speech Processing</subject><ispartof>The Journal of fourier analysis and applications, 2024-06, Vol.30 (3), Article 36</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-7d9ce92d70de2ae273256406ec40aedc405983665060be684ba66f529a2267cc3</cites><orcidid>0000-0002-9028-8137</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00041-024-10095-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-024-10095-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,782,786,27933,27934,41497,42566,51328</link.rule.ids></links><search><creatorcontrib>Gan, Shengwen</creatorcontrib><title>Small Cap Square Function Estimates</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) \| f γ \| 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We find sharp upper and lower bounds of the constant C α , p ( R ) .</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Estimates</subject><subject>Fourier Analysis</subject><subject>Lower bounds</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kF9LwzAUxYMoOKdfwKfCnqM3SXPTPErZnDDwYfocsjSVja7tkhbmtzdawTdf7h8459zLj5B7Bg8MQD1GAMgZBZ7TtGtJzxdkxqRgVBaSXaYZUKcZ9TW5ifEAwJlQYkYW26Ntmqy0fbY9jTb4bDW2bth3bbaMw_5oBx9vyVVtm-jvfvucvK-Wb-Wabl6fX8qnDXUcYKCq0s5rXimoPLeeK8El5oDe5WB9larUhUCUgLDzWOQ7i1hLri3nqJwTc7KYcvvQnUYfB3PoxtCmk0YAYoGSqSKp-KRyoYsx-Nr0If0ZPg0D8w3DTDBMgmF-YJhzMonJFJO4_fDhL_of1xdgLF_8</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Gan, Shengwen</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9028-8137</orcidid></search><sort><creationdate>20240601</creationdate><title>Small Cap Square Function Estimates</title><author>Gan, Shengwen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-7d9ce92d70de2ae273256406ec40aedc405983665060be684ba66f529a2267cc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Estimates</topic><topic>Fourier Analysis</topic><topic>Lower bounds</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gan, Shengwen</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gan, Shengwen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Small Cap Square Function Estimates</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>30</volume><issue>3</issue><artnum>36</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) \| f γ \| 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We find sharp upper and lower bounds of the constant C α , p ( R ) .</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-024-10095-x</doi><orcidid>https://orcid.org/0000-0002-9028-8137</orcidid></addata></record>
fulltext	fulltext
identifier	ISSN: 1069-5869
ispartof	The Journal of fourier analysis and applications, 2024-06, Vol.30 (3), Article 36
issn	1069-5869 1531-5851
language	eng
recordid	cdi_proquest_journals_3066865178
source	SpringerNature Journals
subjects	Abstract Harmonic Analysis Approximations and Expansions Estimates Fourier Analysis Lower bounds Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing
title	Small Cap Square Function Estimates
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-02T13%3A36%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Small%20Cap%20Square%20Function%20Estimates&rft.jtitle=The%20Journal%20of%20fourier%20analysis%20and%20applications&rft.au=Gan,%20Shengwen&rft.date=2024-06-01&rft.volume=30&rft.issue=3&rft.artnum=36&rft.issn=1069-5869&rft.eissn=1531-5851&rft_id=info:doi/10.1007/s00041-024-10095-x&rft_dat=%3Cproquest_cross%3E3066865178%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3066865178&rft_id=info:pmid/&rfr_iscdi=true