In this paper atomic decomposition theorems of martingales are considered. In particular, three atomic decomposition theorems for Lorentz martingale spacesHs p,q, Qp,q andDp,q, where 0 < p < 1, and 0 < q 1, are proved. As a consequence of these decompositions, the authors obtain a sufficient condition for a sublinear operator T, defined on the previous Lorentz martingale spaces Hs p,q, Qp,q and Dp,q and taking values in Lorentz spaces Lr, to be bounded. Also, a restricted weak-type interpolation theorem is established.
Marraffa, V. (2010). MR2541232 (2010j:60101) Yong, Jiao; Lihua, Peng; Peide, Liu Atomic decompositions of Lorentz martingale spaces and applications. J. Funct. Spaces Appl. 7 (2009), no. 2, 153–166. (Reviewer: Valeria Marraffa), 60G46 (46B70 46E15).
MR2541232 (2010j:60101) Yong, Jiao; Lihua, Peng; Peide, Liu Atomic decompositions of Lorentz martingale spaces and applications. J. Funct. Spaces Appl. 7 (2009), no. 2, 153–166. (Reviewer: Valeria Marraffa), 60G46 (46B70 46E15)
MARRAFFA, Valeria
2010-01-01
Abstract
In this paper atomic decomposition theorems of martingales are considered. In particular, three atomic decomposition theorems for Lorentz martingale spacesHs p,q, Qp,q andDp,q, where 0 < p < 1, and 0 < q 1, are proved. As a consequence of these decompositions, the authors obtain a sufficient condition for a sublinear operator T, defined on the previous Lorentz martingale spaces Hs p,q, Qp,q and Dp,q and taking values in Lorentz spaces Lr, to be bounded. Also, a restricted weak-type interpolation theorem is established.
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