English

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 HsH^s implies that ss 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}
}
R2 v1 2026-06-21T13:13:29.778Z