New local T 1 theorems on non-homogeneous spaces
Villarroya, Paco (Santa Clara University (Santa Clara, Estats Units d'Amèrica). Department of Applied Mathematics)

Date:	2024
Abstract:	We develop new local T1 theorems to characterize Calder'on-Zygmund operators that extend boundedly or compactly on Lp(Rn, µ), with µ a measure of power growth. The results, whose proofs do not require random grids, have weaker hypotheses than previously known local T1 theorems since they only require a countable collection of testing functions. Moreover, a further extension of this work allows the use of testing functions supported on cubes of different dimensions. As a corollary, we describe the measures µ of the complex plane for which the Cauchy integral defines a compact operator on Lp(C, µ).
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Calderón-Zygmund operator ; Compact operator ; Non-doubling radon measures ; Cauchy integral
Published in:	Publicacions matemàtiques, Vol. 68 Núm. 2 (2024) , p. 445-506 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/430120

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