On the existence of double singular integrals for kernels without smoothness
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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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 439-445
- MSC: Primary 47.70; Secondary 42.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276838-2
- MathSciNet review: 0276838