Atomic Decompositions Of Weighted Martingale Spaces With Variable Exponents

This paper deals with the method of atomic decomposition of weighted martingale spaces with variable exponents is studied,the main content includes atomic decomposition of martingale spaces with variable exponents,atomic decomposition of weighted martingale spaces with variable exponents and extrapolation of weighted martingale spaces with variable exponents,interpolation of banach-valued Orlicz-Lorentz quasi martingale spaces.The main content of this paper is divided into two parts.The first part summarized the preliminary knowledge of the martingale theory with variable exponents,divided into change the Lebesgue space with variable exponents and martingale spaces with variable exponents two parts to introduce.Content mainly includes the Lebesgue space with variable exponents norm,module function,the classical theory of extrapolation and the expansion of changing index case,The contents of martingale spaces with variable exponents mainly include the atomic decomposition of martingale,the stop time and atomic decomposition of martingale spaces with variable exponents,which will also prepare us to introduce atomic decomposition of weighted martingale spaces with variable exponents.The second part is the main research content of this article,first,we introduce extrapolation of weighted martingale spaces with variable exponents and weighted martingale spaces with variable exponents of some marker and the fundamental lemma,we to expand atomic decomposition of weighted martingale spaces with variable exponents theory,studies the atomic decomposition theory of a class of weighted cases,and the corresponding results are obtained.Then we depict extrapolation of weighted martingale spaces with variable exponents,proved that weighted martingale spaces with variable exponents several theorems of extrapolation.The third part is the research content of this paper.here using function parameters,the Lorentz martingale space a lot of conclusions to generated by the Banach-valued Lorent-Orlicz regular quasi martingale Spaces,forming a new interpolation theory.The innovation points of this paper are as follows:(1)Atomic decomposition method is applied to study martingale Spaces and weighted martingale space with variable exponents,set up the relationship between the different martingale Spaces with variable exponents,will before the conclusion of martingale space to expand to a broader on the martingale space with variable exponents.(2)We use the tool of function parameter to extend the relevant conclusions of Lorentz space and obtain the real interpolation of the new banach value orlicz-lorentz.