Vector-valued weak martingale Hardy spaces and atomic decompositions |
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| Authors: | Y -L Hou Y -B Ren |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China;(2) Department of Mathematics & Physics, Henan University of Science and Technology, Luoyang, 471003, P.R. China |
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| Abstract: | Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w
p
Σα(X), w
p
Q
α(X) and wD
α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued
weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the
operators f*, S
(p)(f) and σ(p)(f) are obtained.
This research was supported by the National Science Foundation of China (No. 10371093). |
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| Keywords: | martingale weak Hardy space atomic decomposition Banach space |
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