English

Some remarks on extrapolation with "flat" weights

Classical Analysis and ODEs 2012-04-19 v1

Abstract

We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{p_{0}}(w), for all "flat" weights, w in A_{p_{0}}, 1 < p_{0} <\infty, then for p in some small neighborhood around p_{0}, and all "flat" A_{p} weights, w, the operator is weakly bounded on L^{p}(w), and as a result we get strong type estimates for the operator.

Keywords

Cite

@article{arxiv.1204.3963,
  title  = {Some remarks on extrapolation with "flat" weights},
  author = {Nicholas Boros and Nikolaos Pattakos and Alexander Volberg},
  journal= {arXiv preprint arXiv:1204.3963},
  year   = {2012}
}

Comments

10 pages

R2 v1 2026-06-21T20:51:09.999Z