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Volume 35, Issue 4
Boundedness for a Class of Operators on Weighted Morrey Space with RD-Measure

Xiaona Cui, Yongjin Lu & Mengmeng Li

DOI: 10.4208/jpde.v35.n4.7

J. Part. Diff. Eq., 35 (2022), pp. 395-408.

Published online: 2022-10

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  • Abstract

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's condition.

  • Keywords

Weighted Morrey space, RD-measure, commutator.

  • AMS Subject Headings

35Q30, 35B40, 35B41, 76D03, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cxn009@126.com (Xiaona Cui)

ylu2@oakland.edu (Yongjin Lu)

hsdlmm@163.com (Mengmeng Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-395, author = {Cui , XiaonaLu , Yongjin and Li , Mengmeng}, title = {Boundedness for a Class of Operators on Weighted Morrey Space with RD-Measure}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {4}, pages = {395--408}, abstract = {

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's condition.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n4.7}, url = {http://global-sci.org/intro/article_detail/jpde/21056.html} }
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 -

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's condition.

Cui , XiaonaLu , Yongjin and Li , Mengmeng. (2022). Boundedness for a Class of Operators on Weighted Morrey Space with RD-Measure. Journal of Partial Differential Equations. 35 (4). 395-408. doi:10.4208/jpde.v35.n4.7
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