An Extrapolation Theorem on Martingale Spaces with A_p Weights  

作　　者：FAN Liping LIU Peide 

机构地区：[1]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2009年第6期465-469,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(10671147)

摘　　要：In this paper, we prove an extrapolation theorem of operators in martingale spaces with Ap weights, which shows that for operators T defined on martingale space Lu^I, if T is bounded on martingale space L^P0 （w） for some 1 〈 P0 〈 ∞ 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 Ap weights and prove that if w ∈ AI, then the maximal operator M is bounded on L^p,q（w） with 1〈p〈∞, 1〈q≤∞.In this paper, we prove an extrapolation theorem of operators in martingale spaces with Ap weights, which shows that for operators T defined on martingale space Lu^I, if T is bounded on martingale space L^P0 （w） for some 1 〈 P0 〈 ∞ 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 Ap weights and prove that if w ∈ AI, then the maximal operator M is bounded on L^p,q（w） with 1〈p〈∞, 1〈q≤∞.

关 键 词：MARTINGALE WEIGHT maximal operator 

分 类 号：O174.52[理学—数学] O211.6[理学—基础数学]