English

A two weight theorem for fractional singular integrals in higher dimension

Classical Analysis and ODEs 2014-03-18 v8

Abstract

We prove a two weight theorem for alpha-fractional singular integrals in higher dimensions, assuming energy side conditions. We also show that reversal of the Energy Lemma fails for the vector Riesz transforms in the plane, as well as other collections of convolution Calderon-Zygmund operators in the plane, and when alpha = 1, even for the infinite vector of all classical 1-fractional Calderon-Zygmund operators.

Keywords

Cite

@article{arxiv.1305.5104,
  title  = {A two weight theorem for fractional singular integrals in higher dimension},
  author = {Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
  journal= {arXiv preprint arXiv:1305.5104},
  year   = {2014}
}

Comments

This paper has been withdrawn by the authors due to mistakes in the proof and is superceded by arXiv:1302.5093v7 and arXiv:1401.0467v6

R2 v1 2026-06-22T00:20:26.370Z