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.
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