Sharp $L^p$ estimates of powers of the complex Riesz transform
Math. Ann. 386 (2023), 1081-1125 Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the $L^p$ norms of $k$-th powers of the operator $R_2+iR_1$ behave exactly as $|k|^{1-2/p}p$, uniformly in $k\in\mathbb{Z}\backslash\{0\}$, $p\geq2$. This gives a complete asymptotic answer to...
Saved in:
| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
17.09.2021
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Math. Ann. 386 (2023), 1081-1125 Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the
$L^p$ norms of $k$-th powers of the operator $R_2+iR_1$ behave exactly as
$|k|^{1-2/p}p$, uniformly in $k\in\mathbb{Z}\backslash\{0\}$, $p\geq2$. This
gives a complete asymptotic answer to a question suggested by Iwaniec and
Martin in 1996. The main novelty are the lower estimates, of which we give
three different proofs. We also conjecture the exact value of
$\|(R_2+iR_1)^k\|_p$. Furthermore, we establish the sharp behaviour of weak
$(1,1)$ constants of $(R_2+iR_1)^k$ and an $L^\infty$ to $BMO$ estimate that is
sharp up to a logarithmic factor. |
|---|---|
| AbstractList | Math. Ann. 386 (2023), 1081-1125 Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the
$L^p$ norms of $k$-th powers of the operator $R_2+iR_1$ behave exactly as
$|k|^{1-2/p}p$, uniformly in $k\in\mathbb{Z}\backslash\{0\}$, $p\geq2$. This
gives a complete asymptotic answer to a question suggested by Iwaniec and
Martin in 1996. The main novelty are the lower estimates, of which we give
three different proofs. We also conjecture the exact value of
$\|(R_2+iR_1)^k\|_p$. Furthermore, we establish the sharp behaviour of weak
$(1,1)$ constants of $(R_2+iR_1)^k$ and an $L^\infty$ to $BMO$ estimate that is
sharp up to a logarithmic factor. |
| Author | Dragičević, Oliver Carbonaro, Andrea Kovač, Vjekoslav |
| Author_xml | – sequence: 1 givenname: Andrea surname: Carbonaro fullname: Carbonaro, Andrea – sequence: 2 givenname: Oliver surname: Dragičević fullname: Dragičević, Oliver – sequence: 3 givenname: Vjekoslav surname: Kovač fullname: Kovač, Vjekoslav |
| BackLink | https://doi.org/10.48550/arXiv.2109.08369$$DView paper in arXiv https://doi.org/10.1007/s00208-022-02419-3$$DView published paper (Access to full text may be restricted) |
| BookMark | eNrjYmDJy89LZWCQNDTQM7EwNTXQTyyqyCzTMzI0sNQzsDA2s-RksAvOSCwqUFDxiStQUUgtLsnMTSxJLVbIT1MoyC9PLQKzSjJSFZLzcwtyUisUgjJTi6sUSooS84rT8otyeRhY0xJzilN5oTQ3g7yba4izhy7YpviCIqB5RZXxIBvjwTYaE1YBAHBGN10 |
| ContentType | Journal Article |
| Copyright | http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.2109.08369 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 2109_08369 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-arxiv_primary_2109_083693 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:48:08 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-arxiv_primary_2109_083693 |
| OpenAccessLink | https://arxiv.org/abs/2109.08369 |
| ParticipantIDs | arxiv_primary_2109_08369 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-09-17 |
| PublicationDateYYYYMMDD | 2021-09-17 |
| PublicationDate_xml | – month: 09 year: 2021 text: 2021-09-17 day: 17 |
| PublicationDecade | 2020 |
| PublicationYear | 2021 |
| Score | 3.645491 |
| SecondaryResourceType | preprint |
| Snippet | Math. Ann. 386 (2023), 1081-1125 Let $R_{1,2}$ be scalar Riesz transforms on $\mathbb{R}^2$. We prove that the
$L^p$ norms of $k$-th powers of the operator... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Classical Analysis and ODEs |
| Title | Sharp $L^p$ estimates of powers of the complex Riesz transform |
| URI | https://arxiv.org/abs/2109.08369 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwY2BQsUxOTjZNSrHUtTRPMtI1STNK07UERoZuciKwg2uenJJiZgbaKOzrZ-YRauIVYRrBxKAA2wuTWFSRWQY5HzipWB_YH7HUA52fbMnMwGxkBFqy5e4fAZmcBB_FBVWPUAdsY4KFkCoJN0EGfmjrTsEREh1CDEypeSIMdqBDkQsUVHziClQUQIda5ILadwr5aQoF4CvKQCxgM0wBvLo7tUIhCNh5rVIogbUoRRnk3VxDnD10wTbGF0COh4gHOSYe7BhjMQYWYCc-VYJBITnFMiXJwswwydwoGdhlMwcWKxYWSRbJRuapyYYmRuaSDBK4TJHCLSXNwGUEWmMButLAXIaBpaSoNFUWWEmWJMmBQwoA-AZr8g |
| link.rule.ids | 228,230,783,888 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sharp+%24L%5Ep%24+estimates+of+powers+of+the+complex+Riesz+transform&rft.au=Carbonaro%2C+Andrea&rft.au=Dragi%C4%8Devi%C4%87%2C+Oliver&rft.au=Kova%C4%8D%2C+Vjekoslav&rft.date=2021-09-17&rft_id=info:doi/10.48550%2Farxiv.2109.08369&rft.externalDocID=2109_08369 |