New local T 1 theorems on non-homogeneous spaces

• Villarroya, Paco ^[1]
  1. [1] Santa Clara University (Santa Clara, Estats Units d'Amèrica). Department of Applied Mathematics,
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 2, 2024, págs. 445-506
• Idioma: inglés
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• Resumen

  • 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).