Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals
Let r > 4 3 and let Ω ∈ L r ( S 2 n - 1 ) have vanishing integral. We show that the bilinear rough singular integral T Ω ( f , g ) ( x ) = p.v. ∫ R n ∫ R n Ω ( ( y , z ) / | ( y , z ) | ) | ( y , z ) | 2 n f ( x - y ) g ( x - z ) d y d z , satisfies a sparse bound by ( p , p , p )-averages, whe...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2022-12, Vol.28 (6), Article 80 |
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| creator | Grafakos, Loukas Wang, Zhidan Xue, Qingying |
| description | Let
r
>
4
3
and let
Ω
∈
L
r
(
S
2
n
-
1
)
have vanishing integral. We show that the bilinear rough singular integral
T
Ω
(
f
,
g
)
(
x
)
=
p.v.
∫
R
n
∫
R
n
Ω
(
(
y
,
z
)
/
|
(
y
,
z
)
|
)
|
(
y
,
z
)
|
2
n
f
(
x
-
y
)
g
(
x
-
z
)
d
y
d
z
,
satisfies a sparse bound by (
p
,
p
,
p
)-averages, where
p
is bigger than a certain number explicitly related to
r
and
n
. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels. |
| doi_str_mv | 10.1007/s00041-022-09973-z |
| format | Article |
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r
>
4
3
and let
Ω
∈
L
r
(
S
2
n
-
1
)
have vanishing integral. We show that the bilinear rough singular integral
T
Ω
(
f
,
g
)
(
x
)
=
p.v.
∫
R
n
∫
R
n
Ω
(
(
y
,
z
)
/
|
(
y
,
z
)
|
)
|
(
y
,
z
)
|
2
n
f
(
x
-
y
)
g
(
x
-
z
)
d
y
d
z
,
satisfies a sparse bound by (
p
,
p
,
p
)-averages, where
p
is bigger than a certain number explicitly related to
r
and
n
. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-022-09973-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Estimates ; Fourier Analysis ; Integrals ; 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, 2022-12, Vol.28 (6), Article 80</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor 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><rights>COPYRIGHT 2022 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-1ea4739229e02354932c461644169a1d9aea01e05089afd3be9892c6c7ce39d43</citedby><cites>FETCH-LOGICAL-c288t-1ea4739229e02354932c461644169a1d9aea01e05089afd3be9892c6c7ce39d43</cites><orcidid>0000-0002-1646-9925 ; 0000-0001-7094-9201 ; 0000-0001-8327-5066</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/s00041-022-09973-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-022-09973-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27926,27927,41490,42559,51321</link.rule.ids></links><search><creatorcontrib>Grafakos, Loukas</creatorcontrib><creatorcontrib>Wang, Zhidan</creatorcontrib><creatorcontrib>Xue, Qingying</creatorcontrib><title>Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>Let
r
>
4
3
and let
Ω
∈
L
r
(
S
2
n
-
1
)
have vanishing integral. We show that the bilinear rough singular integral
T
Ω
(
f
,
g
)
(
x
)
=
p.v.
∫
R
n
∫
R
n
Ω
(
(
y
,
z
)
/
|
(
y
,
z
)
|
)
|
(
y
,
z
)
|
2
n
f
(
x
-
y
)
g
(
x
-
z
)
d
y
d
z
,
satisfies a sparse bound by (
p
,
p
,
p
)-averages, where
p
is bigger than a certain number explicitly related to
r
and
n
. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Estimates</subject><subject>Fourier Analysis</subject><subject>Integrals</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>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhQdRsFb_gKsB11NvHvPIstaqhaJgFZchZu5MU9qkJjML--uNjuBOsjiHcL7cm5MklwQmBKC8DgDASQaUZiBEybLDUTIiOSNZXuXkOHooRPSFOE3OQtgAUMJKNkoeV3vlA6a3bmes6oyzqbJ1-oamXXdYp_PQmZ3qMKSN8-mz69t1emO2xqLy6crYtt9Gs7Adtl5tw3ly0kTBi18dJ69385fZQ7Z8ul_MpstM06rqMoKKl0xQKhAoy7lgVPOCFJyTQihSC4UKCEIOlVBNzd5RVILqQpcamag5GydXw7t77z56DJ3cuN7bOFLSkhbAgTMWU5Mh1aotSmMb13ml46lxZ7Sz2Jh4Py0po1BUhESADoD2LgSPjdz7-H3_KQnI76LlULSMRcufouUhQmyAQgzbFv3fLv9QXyZkf9Q</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Grafakos, Loukas</creator><creator>Wang, Zhidan</creator><creator>Xue, Qingying</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1646-9925</orcidid><orcidid>https://orcid.org/0000-0001-7094-9201</orcidid><orcidid>https://orcid.org/0000-0001-8327-5066</orcidid></search><sort><creationdate>20221201</creationdate><title>Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals</title><author>Grafakos, Loukas ; Wang, Zhidan ; Xue, Qingying</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-1ea4739229e02354932c461644169a1d9aea01e05089afd3be9892c6c7ce39d43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Estimates</topic><topic>Fourier Analysis</topic><topic>Integrals</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>Grafakos, Loukas</creatorcontrib><creatorcontrib>Wang, Zhidan</creatorcontrib><creatorcontrib>Xue, Qingying</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>Grafakos, Loukas</au><au>Wang, Zhidan</au><au>Xue, Qingying</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>28</volume><issue>6</issue><artnum>80</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>Let
r
>
4
3
and let
Ω
∈
L
r
(
S
2
n
-
1
)
have vanishing integral. We show that the bilinear rough singular integral
T
Ω
(
f
,
g
)
(
x
)
=
p.v.
∫
R
n
∫
R
n
Ω
(
(
y
,
z
)
/
|
(
y
,
z
)
|
)
|
(
y
,
z
)
|
2
n
f
(
x
-
y
)
g
(
x
-
z
)
d
y
d
z
,
satisfies a sparse bound by (
p
,
p
,
p
)-averages, where
p
is bigger than a certain number explicitly related to
r
and
n
. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-022-09973-z</doi><orcidid>https://orcid.org/0000-0002-1646-9925</orcidid><orcidid>https://orcid.org/0000-0001-7094-9201</orcidid><orcidid>https://orcid.org/0000-0001-8327-5066</orcidid></addata></record> |
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| ispartof | The Journal of fourier analysis and applications, 2022-12, Vol.28 (6), Article 80 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_proquest_journals_2726040433 |
| source | SpringerNature Journals |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Estimates Fourier Analysis Integrals Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| title | Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals |
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