Square function and Riesz transform in non-integer dimensions

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

Cited by in corpus (1)

• On the boundedness of non-integer dimension Calderón-Zygmund Operators with antisymmetric kernels