Bounds for discrete multilinear spherical maximal functions in higher dimensions

We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r>d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in...

Full description

Saved in:
Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2021-06, Vol.53 (3), p.855-860
Main Authors: Anderson, Theresa C., Palsson, Eyvindur Ari
Format: Article
Language:English
Subjects:
11Dxx
42Bxx (primary)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3
cites cdi_FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3
container_end_page 860
container_issue 3
container_start_page 855
container_title The Bulletin of the London Mathematical Society
container_volume 53
creator Anderson, Theresa C.
Palsson, Eyvindur Ari
description We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r>d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions d=3,4, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree k, ℓ‐linear operators.
doi_str_mv 10.1112/blms.12465
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_blms_12465</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>BLMS12465</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3</originalsourceid><addsrcrecordid>eNp9kM1LxDAQxYMoWFcv_gU5C10zSdu0R3fxCyoK6rmk6cSN9GNJWnT_e1Pr2cPw4M3vDcMj5BLYGgD4dd12fg08ydIjEkGSFTEHzo5JxBhP4owV4pScef_JGAgmISIvm2HqG0_N4GhjvXY4Iu2mdrSt7VE56vc7dFarlnbq23ZBzdTr0Q69p7anO_sR9iHaYe9n85ycGNV6vPjTFXm_u33bPsTl8_3j9qaMNZcijXkiNceai7SQClTNRMZRNDLFXBnIhKoTxXMjNSKaYJu0hjBGqAZlXhixIlfLXe0G7x2aau_Ce-5QAavmLqq5i-q3iwDDAn_ZFg__kNWmfHpdMj_YH2Qk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Bounds for discrete multilinear spherical maximal functions in higher dimensions</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Anderson, Theresa C. ; Palsson, Eyvindur Ari</creator><creatorcontrib>Anderson, Theresa C. ; Palsson, Eyvindur Ari</creatorcontrib><description>We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r&gt;d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions d=3,4, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree k, ℓ‐linear operators.</description><identifier>ISSN: 0024-6093</identifier><identifier>EISSN: 1469-2120</identifier><identifier>DOI: 10.1112/blms.12465</identifier><language>eng</language><subject>11Dxx ; 42Bxx (primary)</subject><ispartof>The Bulletin of the London Mathematical Society, 2021-06, Vol.53 (3), p.855-860</ispartof><rights>2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3</citedby><cites>FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27911,27912</link.rule.ids></links><search><creatorcontrib>Anderson, Theresa C.</creatorcontrib><creatorcontrib>Palsson, Eyvindur Ari</creatorcontrib><title>Bounds for discrete multilinear spherical maximal functions in higher dimensions</title><title>The Bulletin of the London Mathematical Society</title><description>We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r&gt;d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions d=3,4, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree k, ℓ‐linear operators.</description><subject>11Dxx</subject><subject>42Bxx (primary)</subject><issn>0024-6093</issn><issn>1469-2120</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1LxDAQxYMoWFcv_gU5C10zSdu0R3fxCyoK6rmk6cSN9GNJWnT_e1Pr2cPw4M3vDcMj5BLYGgD4dd12fg08ydIjEkGSFTEHzo5JxBhP4owV4pScef_JGAgmISIvm2HqG0_N4GhjvXY4Iu2mdrSt7VE56vc7dFarlnbq23ZBzdTr0Q69p7anO_sR9iHaYe9n85ycGNV6vPjTFXm_u33bPsTl8_3j9qaMNZcijXkiNceai7SQClTNRMZRNDLFXBnIhKoTxXMjNSKaYJu0hjBGqAZlXhixIlfLXe0G7x2aau_Ce-5QAavmLqq5i-q3iwDDAn_ZFg__kNWmfHpdMj_YH2Qk</recordid><startdate>202106</startdate><enddate>202106</enddate><creator>Anderson, Theresa C.</creator><creator>Palsson, Eyvindur Ari</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202106</creationdate><title>Bounds for discrete multilinear spherical maximal functions in higher dimensions</title><author>Anderson, Theresa C. ; Palsson, Eyvindur Ari</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>11Dxx</topic><topic>42Bxx (primary)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Anderson, Theresa C.</creatorcontrib><creatorcontrib>Palsson, Eyvindur Ari</creatorcontrib><collection>CrossRef</collection><jtitle>The Bulletin of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Anderson, Theresa C.</au><au>Palsson, Eyvindur Ari</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bounds for discrete multilinear spherical maximal functions in higher dimensions</atitle><jtitle>The Bulletin of the London Mathematical Society</jtitle><date>2021-06</date><risdate>2021</risdate><volume>53</volume><issue>3</issue><spage>855</spage><epage>860</epage><pages>855-860</pages><issn>0024-6093</issn><eissn>1469-2120</eissn><abstract>We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r&gt;d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions d=3,4, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree k, ℓ‐linear operators.</abstract><doi>10.1112/blms.12465</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0024-6093
ispartof The Bulletin of the London Mathematical Society, 2021-06, Vol.53 (3), p.855-860
issn 0024-6093
1469-2120
language eng
recordid cdi_crossref_primary_10_1112_blms_12465
source Wiley-Blackwell Read & Publish Collection
subjects 11Dxx
42Bxx (primary)
title Bounds for discrete multilinear spherical maximal functions in higher dimensions
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T01%3A20%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bounds%20for%20discrete%20multilinear%20spherical%20maximal%20functions%20in%20higher%20dimensions&rft.jtitle=The%20Bulletin%20of%20the%20London%20Mathematical%20Society&rft.au=Anderson,%20Theresa%20C.&rft.date=2021-06&rft.volume=53&rft.issue=3&rft.spage=855&rft.epage=860&rft.pages=855-860&rft.issn=0024-6093&rft.eissn=1469-2120&rft_id=info:doi/10.1112/blms.12465&rft_dat=%3Cwiley_cross%3EBLMS12465%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2735-247c2eb23597a1ab0362e3d75e8af163ab4a28f7ceeefd75f5b1f5bf3ade789f3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true