分数次积分交换子在非齐Morrey空间上的紧性

本文主要建立由分数次积分$I_{\gamma}$与函数$b\in\mathrm{Lip}_{\beta}(\mu)$生成的交换子$b, I_{\gamma}]$在以满足几何双倍与上部双倍条件的非齐度量测度空间为底空间的Morrey空间上紧性的充要条件.在假设控制函数$\lambda$满足逆双倍条件下,证明了交换子$b,I_{\gamma}]$为从Morrey空间$M^{p}_{q}(\mu)$到$M^{s}_{t}(\mu)$紧性当且仅当$b\in\mathrm{Lip}_{\beta}(\mu)$.

Grand Generalized Weighted Morrey Spaces for RD-Spaces

Let $(X,d,\mu)$ be an RD-space satisfying both the doubling condition in the sense of\\ Coifman and Weiss and the reverse doubling condition. In this setting, the author obtains the\\ definition of grand generalized weighted Morrey space on $(X,d,\mu)$, and also investigates some p-\\roperties of these spaces. As an application, the boundedness of the Hardy-Littlewood maximal operator and the $\theta$-type Calder\''{o}n-Zygmund operator on spaces $\mathcal{L}^{p),\varphi,\Phi}_{\omega}(X)$ is also obtained.