Title of article :
Fractional maximal commutator on Orlicz spaces for the Dunkl operator on the real line
Author/Authors :
Mammadov, Yagub Y. Nakhchivan Teacher-Training Institute, Azerbaijan , Muslumova, Fatma A. Department of Informatics - Nakhchivan State University, Azerbaijan , Safarov, Zaman V. Azerbaijan State Oil and Industry University, Baku, Azerbaijan
Abstract :
On the real line, the Dunkl operators are differential-difference operators associated with the reflection group Z2 on R. In this paper, we find necessary and sufficient conditions for the boundedness of the fractional maximal operator Mα,ν on
Orlicz spaces LΦ(R, dmν). As an application of this result we show that b ∈ BMO(R, dmν) if and only
if the fractional maximal commutator Mb,α,ν is bounded on Orlicz spaces LΦ(R, dmν).
Keywords :
Fractional maximal operator , Orlicz space , Dunkl operator , commutator , BMO
Journal title :
Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
