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arXiv · 1906.10782

A limited-range Calder\'on-Zygmund theorem

Loukas Grafakos·Cody B. Stockdale
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Abstract

For a limited range of indices $p$, we obtain $L^p(\mathbb{R}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical H\"ormander smoothness estimate. These operators are assumed to be bounded (or weakly bounded) on $L^{s}(\mathbb{R}^n)$ for some index $s$. Our estimates are obtained via interpolation from the appropriate weak-type estimates. We provide two proofs of this result. One proof is based on the Calder\'on-Zygmund decomposition, while the other uses ideas of Nazarov, Treil, and Volberg.

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Loukas Grafakos, Cody B. Stockdale. 2019-06-25. A limited-range Calder\'on-Zygmund theorem. https://arxiv.org/abs/1906.10782

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