An extrapolation theorem on martingale spaces with Ap weights |
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Authors: | Liping Fan Peide Liu |
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Institution: | 1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China
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Abstract: | In this paper, we prove an extrapolation theorem of operators in martingale spaces with A
p
weights, which shows that for operators T defined on martingale space L
u
1
, if T is bounded on martingale space L
p0(w) for some 1 < p
0 < ∞ and every, w∈ A
∞, so it is on L
p,s
(w) for every 1 < p, s < ∞, and w ∈ A
∞. We also get some properties of A
p
weights and prove that if w ∈ A
1, then the maximal operator M is bounded on L
p,q
(w) with 1 < p < ∞, 1 < q ≤ ∞. |
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Keywords: | |
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