TY - JOUR

T1 - Geometric conditions for the L 2 -boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in ℝ d

AU - Girela-Sarrión, Daniel

PY - 2019/3/1

Y1 - 2019/3/1

N2 - © 2019, The Hebrew University of Jerusalem. Let μ be a finite Radon measure in ℝ d with polynomial growth of degree n, although not necessarily n-AD regular. We prove that under some geometric conditions on μ that are closely related to rectifiability and involve the so-called β-numbers of Jones, David and Semmes, all singular integral operators with an odd and sufficiently smooth Calderón-Zygmund kernel are bounded in L 2 (μ). As a corollary, we obtain a lower bound for the Lipschitz harmonic capacity of a compact set in ℝ d only in terms of its metric and geometric properties.

AB - © 2019, The Hebrew University of Jerusalem. Let μ be a finite Radon measure in ℝ d with polynomial growth of degree n, although not necessarily n-AD regular. We prove that under some geometric conditions on μ that are closely related to rectifiability and involve the so-called β-numbers of Jones, David and Semmes, all singular integral operators with an odd and sufficiently smooth Calderón-Zygmund kernel are bounded in L 2 (μ). As a corollary, we obtain a lower bound for the Lipschitz harmonic capacity of a compact set in ℝ d only in terms of its metric and geometric properties.

U2 - 10.1007/s11854-018-0075-2

DO - 10.1007/s11854-018-0075-2

M3 - Article

VL - 137

SP - 339

EP - 372

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

SN - 0021-7670

ER -