A note on failure of energy reversal for classical fractional singular integrals
Classical Analysis and ODEs
2014-03-18 v6
Abstract
For alpha in [0,n) we demonstrate the failure of energy reversal for the vector of alpha-fractional Riesz transforms, and more generally for any vector of alpha-fractional convolution singular integrals having a kernel with vanishing integral on every great circle of the sphere.
Keywords
Cite
@article{arxiv.1401.0467,
title = {A note on failure of energy reversal for classical fractional singular integrals},
author = {Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
journal= {arXiv preprint arXiv:1401.0467},
year = {2014}
}
Comments
24 pages. This version references a correct form of the T1 theorem, corrects typos and uses Bochner's theorem to complete the proof for the missing range of alpha, and also points out an easy extension to higher dimensions. arXiv admin note: text overlap with arXiv:1305.5104