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Some remarks on extrapolation with "flat" weights

Authors
  • Boros, Nicholas
  • Pattakos, Nikolaos
  • Volberg, Alexander
Type
Preprint
Publication Date
Apr 17, 2012
Submission Date
Apr 17, 2012
Identifiers
arXiv ID: 1204.3963
Source
arXiv
License
Yellow
External links

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.

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