分数次积分交换子在非齐Morrey空间上的紧性

Compactness for Commutator of Fractional Integral on Non-homogeneous Morrey Spaces

中文关键词:  非齐度量测度空间  紧性  分数次积分交换子  $\mathrm{Lip}_{\beta}(\mu)$  Morrey 空间

英文关键词:non-homogeneous metric measure space  compactness  commutator of fractional integral  $\mathrm{Lip}_{\beta}(\mu)$  Morrey space

中文摘要:

      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$b\in\mathrm{Lip}_{\beta}(\mu)$.

英文摘要:

      The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator $[b, I_{\gamma}]$ which is generated by fractional integral $I_{\gamma}$ and function $b\in\mathrm{Lip}_{\beta}(\mu)$ on Morrey space over non-homogeneous metric measure space, which satisfies the geometrically doubling and upper doubling conditions in the sense of Hyt\"{o}nen. Under assumption that the dominating function $\lambda$ satisfies weak reverse doubling condition, the author proves that the commutator $[b,I_{\gamma}]$ is compact from Morrey space $M^{p}_{q}(\mu)$ into Morrey space $M^{s}_{t}(\mu)$ if and only if $b\in\mathrm{Lip}_{\beta}(\mu)$.