Some remarks on extrapolation with "flat" weights

Details Some remarks on extrapolation with "flat" weights Some remarks on extrapolation with "flat" weights

2012-04-18

arxiv.org/abs/1204.3963v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

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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