TY - JOUR
T1 - Boundedness for a Class of Operators on Weighted Morrey Space with RD-Measure
AU - Cui , Xiaona
AU - Lu , Yongjin
AU - Li , Mengmeng
JO - Journal of Partial Differential Equations
VL - 4
SP - 395
EP - 408
PY - 2022
DA - 2022/10
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n4.7
UR - https://global-sci.org/intro/article_detail/jpde/21056.html
KW - Weighted Morrey space, RD-measure, commutator.
AB - <p style="text-align: justify;">In this paper, we study a class of sublinear operators and their commutators with a weighted BMO function. We first give the definition of a weighted Morrey space $L^{p,\kappa}_{\mu,\omega}(X)$ where $X$ is an RD-measure and $\omega$ is the weight function. The weighted Morrey spaces arise from studying the local behavior of solutions to certain partial differential equations. We will show that the aforementioned class of operators and their communtators with a weighted BMO function are bounded in the weighted Morrey space $L^{p,\kappa}_{\mu,\omega}(X)$ provided that the weight function $\omega$ belongs to the $A_p(\mu)$-class and satisfies the reverse Hölder&#39;s condition.</p>