ON THE BOUNDEDNESS OF DUNKL-TYPE FRACTIONAL
INTEGRAL OPERATOR IN THE GENERALIZED
DUNKL-TYPE MORREY SPACES
Yagub Y. Mammadov1, Samira A. Hasanli2
1,2Nakhcivan State University
Nakhchivan City, AZ 7012, AZERBAIJAN

Abstract

First, we prove that the Dunkl-type maximal operator $M_{\alpha}$ is bounded on the generalized Dunkl-type Morrey spaces ${\cal M}_{p,\omega,\alpha}$ for $1<p<\infty$ and from the spaces ${\cal M}_{1,\omega,\alpha}$ to the weak spaces $W{\cal M}_{1,\omega,\alpha}$.

We prove that the Dunkl-type fractional order integral operator $I^{\beta,\alpha},$ $0<\beta <2\alpha+2$ is bounded from the generalized Dunkl-type Morrey spaces ${\cal M}_{p,\omega,\alpha}$ to ${\cal M}_{q,\omega^{p/q},\alpha}$, where ${\beta}/{(2\alpha+2)}=1/p-1/q$, $1<p<(2\alpha+2)/{\beta}$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 2
Year: 2018

DOI: 10.12732/ijam.v31i2.4

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