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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the existence of double singular integrals for kernels without smoothness


Author: T. Walsh
Journal: Proc. Amer. Math. Soc. 28 (1971), 439-445
MSC: Primary 47.70; Secondary 42.00
MathSciNet review: 0276838
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Abstract: Calderón and Zygmund have proved the pointwise convergence of singular integrals in $ {R^n}$ for locally integrable homogeneous kernels whose even part is locally in $ L$ log $ L$ by change to polar coordinates and use of the boundedness in $ {L^p}$ of the maximal operator of the one-dimensional Hilbert transformation. The present note shows how analogous results for double singular integrals can be derived from boundedness of the maximal operator of the double Hilbert transform.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0276838-2
PII: S 0002-9939(1971)0276838-2
Keywords: Double singular integrals, kernels without smoothness, maximal function
Article copyright: © Copyright 1971 American Mathematical Society