English

Sharp weighted bounds without testing or extrapolation

Classical Analysis and ODEs 2012-11-16 v2 Functional Analysis

Abstract

We give a short proof of the sharp weighted bound for sparse operators that holds for all pp, 1<p<1<p<\infty. By recent developments this implies the bounds hold for any Calder\'on-Zygmund operator. The novelty of our approach is that we avoid two techniques that are present in other proofs: two weight inequalities and extrapolation. Our techniques are applicable to fractional integral operators as well.

Keywords

Cite

@article{arxiv.1210.4207,
  title  = {Sharp weighted bounds without testing or extrapolation},
  author = {Kabe Moen},
  journal= {arXiv preprint arXiv:1210.4207},
  year   = {2012}
}

Comments

Minor errors corrected. Final version

R2 v1 2026-06-21T22:22:13.850Z