The fractional Riesz transform and their commutator in Dunkl setting
Yanping Chen, Xueting Han, Liangchuan Wu
TL;DR
This paper investigates the boundedness and compactness of fractional Riesz transforms and their commutators within the Dunkl setting, establishing conditions related to BMO and VMO spaces.
Contribution
It provides new necessary and sufficient conditions for the boundedness and compactness of commutators of fractional Riesz transforms in Dunkl analysis.
Findings
Boundedness characterized by BMO spaces
Compactness characterized by VMO spaces
Conditions established for Dunkl and Euclidean metrics
Abstract
In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness of their commutator with respect to the central BMO space associated with Euclidean metric and the BMO space associated with Dunkl metric, respectively. Based on this, we further characterize the compactness of the commutator in terms of the corresponding types of VMO spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials