This article is cited in 3 papers

Brief communications

Embeddings of Lorentz Spaces of Vector-Valued Martingales

Yong Jiao^ab, Tao Ma^c, Peide Liu<sup>c

a</sup> Laboratoire de Mathématiques, Université de Franche-Comté, France
^b School of Mathematics Science and Computing Technology, Central South University, Changsha, China
^c School of Mathematics and Statistics, Wuhan University, China

Abstract: We obtain new embedding theorems for Lorentz spaces of vector-valued martingales, thus generalizing the classical martingale inequalities. In contrast to earlier methods, we use martingale transformations defined by sequences of operators and identify the operator $S^{(p)}(f)$ for a martingale $f$ ranging in a Banach space $X$ with the maximal operator for some $\ell^p(X)$-valued martingale transform. The obtained inequalities are closely related to geometric properties of the Banach space in question.

Keywords: martingale Lorentz space, embedding, uniformly convex space, uniformly smooth space.

UDC: 517.9

Received: 31.10.2008

DOI: 10.4213/faa3001

 English version: Functional Analysis and Its Applications, 2010, 44:3, 237–240

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