104 research outputs found
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
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
Characterizations of Lipschitz functions via the commutators of maximal function in Orlicz spaces on stratified Lie groups
We give necessary and sufficient conditions for the boundedness of the
maximal commutators , the commutators of the maximal operator
and the commutators of the sharp maximal operator in Orlicz
spaces on any stratified Lie group when
belongs to Lipschitz spaces . We obtain some
new characterizations for certain subclasses of Lipschitz spaces
.Comment: AMS-LaTeX 22 pages. arXiv admin note: text overlap with
arXiv:1803.0306
Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-morrey spaces
We prove the boundedness of the Hardy-Littlewood maximal operator and their commutators with BMO-coefficients in vanishing generalized Orlicz-Morrey spaces VM Phi,phi(R-n) including weak versions of these spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators involving the Young function Phi(u) and the function phi(x, r) defining the space. No kind of monotonicity condition on phi(x, r) in r is imposed.Ahi Evran University [PYO.FEN.4003.13.003, PYO.FEN.4001.14.017]; Science Development Foundation under Republic of Azerbaijan [EIF-2013-9(15)-46/10/1]; Russian Fund of Basic Research [15-01-02732
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