On the L p-boundedness of Calderón-Zygmund operators
The main result in this paper is that, for singular integral operators associated with standard kernels, local L 1-estimates imply global L p-estimates for every p ∈ (1, ∞). When combined with the result of Melnikov-Verdera, this yields a complete and self-contained proof of the L p-boundedness of t...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0183 |
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| _version_ | 1839623053272678400 |
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| author | Mitrea Dorina Mitrea Marius |
| author_facet | Mitrea Dorina Mitrea Marius |
| author_sort | Mitrea Dorina |
| collection | DOAJ |
| description | The main result in this paper is that, for singular integral operators associated with standard kernels, local L
1-estimates imply global L
p-estimates for every p ∈ (1, ∞). When combined with the result of Melnikov-Verdera, this yields a complete and self-contained proof of the L
p-boundedness of the Cauchy operator on Lipschitz curves and chord-arc curves in the plane. |
| format | Article |
| id | doaj-art-161c8b2cdc7b47f0889c8d5457f9950b |
| institution | Matheson Library |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-161c8b2cdc7b47f0889c8d5457f9950b2025-07-21T06:53:53ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-04-0125247048810.1515/ans-2023-0183On the L p-boundedness of Calderón-Zygmund operatorsMitrea Dorina0Mitrea Marius1Baylor University, Waco, USABaylor University, Waco, USAThe main result in this paper is that, for singular integral operators associated with standard kernels, local L 1-estimates imply global L p-estimates for every p ∈ (1, ∞). When combined with the result of Melnikov-Verdera, this yields a complete and self-contained proof of the L p-boundedness of the Cauchy operator on Lipschitz curves and chord-arc curves in the plane.https://doi.org/10.1515/ans-2023-0183calderón-zygmund theorycauchy operatorahlfors regular setlipschitz curveshardy spacebmoprimary42b2042b3042b3546e30secondary46b7047b90 |
| spellingShingle | Mitrea Dorina Mitrea Marius On the L p-boundedness of Calderón-Zygmund operators Advanced Nonlinear Studies calderón-zygmund theory cauchy operator ahlfors regular set lipschitz curves hardy space bmo primary 42b20 42b30 42b35 46e30 secondary 46b70 47b90 |
| title | On the L
p-boundedness of Calderón-Zygmund operators |
| title_full | On the L
p-boundedness of Calderón-Zygmund operators |
| title_fullStr | On the L
p-boundedness of Calderón-Zygmund operators |
| title_full_unstemmed | On the L
p-boundedness of Calderón-Zygmund operators |
| title_short | On the L
p-boundedness of Calderón-Zygmund operators |
| title_sort | on the l p boundedness of calderon zygmund operators |
| topic | calderón-zygmund theory cauchy operator ahlfors regular set lipschitz curves hardy space bmo primary 42b20 42b30 42b35 46e30 secondary 46b70 47b90 |
| url | https://doi.org/10.1515/ans-2023-0183 |
| work_keys_str_mv | AT mitreadorina onthelpboundednessofcalderonzygmundoperators AT mitreamarius onthelpboundednessofcalderonzygmundoperators |