1,101 research outputs found
On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces
We consider generalized Orlicz-Morrey spaces M_{\Phi,\varphi}(\Rn)
including their weak versions WM_{\Phi,\varphi}(\Rn). In these spaces we
prove the boundedness of the Riesz potential from M_{\Phi,\varphi_1}(\Rn) to
M_{\Psi,\varphi_2}(\Rn) and from M_{\Phi,\varphi_1}(\Rn) to
WM_{\Psi,\varphi_2}(\Rn). As applications of those results, the boundedness
of the commutators of the Riesz potential on generalized Orlicz-Morrey space is
also obtained. In all the cases the conditions for the boundedness are given
either in terms of Zygmund-type integral inequalities on
, which do not assume any assumption on monotonicity
of , in r.Comment: 23 pages. J. Funct. Spaces Appl.(to appear
Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces
We consider generalized Orlicz-Morrey spaces
including their weak versions
. We find the sufficient conditions on the
pairs and which ensures the
boundedness of the fractional maximal operator from
to
and from to
. As applications of those results, the
boundedness of the commutators of the fractional maximal operator
with on the spaces
is also obtained. In all the cases the
conditions for the boundedness are given in terms of supremal-type inequalities
on weights , which do not assume any assumption on monotonicity
of on .Comment: 23 pages. Complex Anal. Oper. Theory (to appear). arXiv admin note:
substantial text overlap with arXiv:1310.660
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