Square function and Riesz transform in non-integer dimensions
Classical Analysis and ODEs
2009-11-01 v1 Functional Analysis
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 implies that is integer.
Cite
@article{arxiv.0906.2666,
title = {Square function and Riesz transform in non-integer dimensions},
author = {Svitlana Mayboroda and Alexander Volberg},
journal= {arXiv preprint arXiv:0906.2666},
year = {2009}
}