Square function and Riesz transform in non-integer dimensions

Svitlana Mayboroda; Alexander Volberg

doi:10.1016/j.crma.2009.09.020

paper

Square function and Riesz transform in non-integer dimensions

arXiv:0906.2666 · doi:10.1016/j.crma.2009.09.020

Abstract

Following a recent paper by X. Tolsa and A. Ruiz de Villa [Non existence of principal values of signed Riesz transforms of non integer dimension, preprint], we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure $H^{s}$ implies that $s$ is integer.

References in corpus (1)

Non existence of principal values of signed Riesz transforms of non integer dimension