New Local T1 Theorems on non-homogeneous spaces

2021/04/02 by Paco Villarroya, Villarroya, Paco
Mathematics · #Advanced Harmonic Analysis Research #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CA

paper · pdf · doi:10.48550/arxiv.2104.01277

arxiv created 2021/04/02 · arxiv updated 2021/04/06

Abstract

We develop new local T1 theorems to characterize Calderón-Zygmund operators that extend boundedly or compactly on L^p(\mathbb Rⁿ,μ) with μ 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 μ of the complex plane for which the Cauchy integral defines a compact operator on L^p(\mathbb C,μ).

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