论文标题
具有可变指数的加权空间的不平等
Inequalities for weighted spaces with variable exponents
论文作者
论文摘要
在本文中，我们获得了具有可变指数的加权Lebesgue空间上的Fefferman-Stein Vector值最大不平等的“非对角线”版本。作为此结果的应用以及[12]中开发的原子分解，我们证明，对于某些指数$ q（\ cdot）$中的$ Q（\ cdot）$ in $ \ nathcal {p}^{\ log}（\ m athbb {r}^{n}^{n> $ H^{ \ frac {1} {q（\ cdot）} + \fracα{n} $。
In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12] we prove, for certain exponents $q(\cdot)$ in $\mathcal{P}^{\log}(\mathbb{R}^{n})$ and certain weights $ω$, that the Riesz potential $I_α$, with $0 < α< n$, can be extended to a bounded operator from $H^{p(\cdot)}_ω(\mathbb{R}^{n})$ into $L^{q(\cdot)}_ω(\mathbb{R}^{n})$, for $\frac{1}{p(\cdot)} := \frac{1}{q(\cdot)} + \fracα{n}$.
