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arXiv · 2104.01277

New Local T1 Theorems on non-homogeneous spaces

Paco Villarroya
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Abstract

We develop new local $T1$ theorems to characterize Calder\'on-Zygmund operators that extend boundedly or compactly on $L^{p}(\mathbb R^{n},\mu)$ with $\mu$ a measure of power growth. The results, whose proofs do not require random grids, allow the use of a countable collection of testing functions. As a corollary, we describe the measures $\mu$ of the complex plane for which the Cauchy integral defines a compact operator on $L^p(\mathbb C,\mu)$.

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Paco Villarroya. 2021-04-02. New Local T1 Theorems on non-homogeneous spaces. https://arxiv.org/abs/2104.01277

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