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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2169-0375 |