Resumen de New local T 1 theorems on non-homogeneous spaces

Paco Villarroya

• 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).