Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting
Year: 2020
Author: Vagif S. Guliyev, Yagub Y. Mammadov, Fatma A. Muslumova
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 45–65
Abstract
On the real line, the Dunkl operators
Dν(f)(x):=df(x)dx+(2ν+1)f(x)−f(−x)2x, ∀x∈R, ∀ν≥−12
are differential-difference operators associated with the reflection group Z2 on R, and on the Rd the Dunkl operators {Dk,j}dj=1 are the differential-difference operators associated with the reflection group Zd2 on Rd.
In this paper, in the setting R we show that b∈BMO(R,dmν) if and only if the maximal commutator Mb,ν is bounded on Orlicz spaces LΦ(R,dmν). Also in the setting Rd we show that b∈BMO(Rd,h2k(x)dx) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ(Rd,h2k(x)dx).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n1.20.03
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 45–65
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Maximal operator Orlicz space Dunkl operator commutator BMO.
Author Details
Vagif S. Guliyev Email
Yagub Y. Mammadov Email
Fatma A. Muslumova Email