Fractional Integral on Martingale Hardy Spaces With Variable Exponents
Fractional Integral on Martingale Hardy Spaces With Variable Exponents
复制标题
DOI：
10.1515/fca-2015-0065
复制
发表时间：
2015
影响因子：
3
通讯作者：
Z. Hao;Y. Jiao
中科院分区：
文献类型：
--
作者：
Z. Hao;Y. Jiao
本文研究了分数次积分算子在概率空间上定义的变指数可料鞅哈代空间上的有界性。更精确地说，设f =（fn）n≥0是概率空间（Ω，F，Ω）上的鞅，Iαf，α > 0是与f有关的分数次积分算子.在合理的假设下，证明了Iαf在变指数鞅哈代空间上有界.我们的方法是原子分解定理在变指数可料鞅哈代空间上的推广。
Abstract In this paper we investigate the boundedness of fractional integral operators on predictable martingale Hardy spaces with variable exponents defined on a probability space. More precisely, let f = (fn)n≥0 be a martingale on probability space (Ω,F, ℙ), and let Iαf, α > 0 be the fractional integral operator associated with f. Under some reasonable assumptions, it is proved that Iαf is bounded on martingale Hardy spaces with variable exponents. Our method is an extension of atomic decomposition theorem to predicable martingale Hardy spaces of variable exponents.