330 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
Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind
In the present paper, we will characterize the boundedness of the generalized
fractional integral operators and the generalized fractional maximal
operators on Orlicz spaces, respectively. Moreover, we will give a
characterization for the Spanne-type boundedness and the Adams-type boundedness
of the operators and on generalized Orlicz--Morrey
spaces, respectively. Also we give criteria for the weak versions of the
Spanne-type boundedness and the Adams-type boundedness of the operators
and on generalized Orlicz--Morrey spaces
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
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
Boundedness of intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces
We shall investigate the boundedness of the intrinsic square functions and
their commutators on generalized weighted Orlicz-Morrey spaces
. In all the cases, the conditions for the
boundedness are given in terms of Zygmund-type integral inequalities on weights
without assuming any monotonicity property of with
fixed.Comment: 21pages. arXiv admin note: text overlap with arXiv:1311.612
Weighted Hardy and potential operators in the generalized Morrey spaces
We study the weighted p -> q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L-p.phi(R-n, w) defined by an almost increasing function phi(r) and radial type weight w(vertical bar x vertical bar). We obtain sufficient conditions, in terms of some integral inequalities imposed on phi and w, for such a p -> q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p -> q-boundedness of the Riesz potential operator. (c) 2010 Elsevier Inc. All rights reserved.Lulea University of Technology; FCT, Portugal [SFRH/BPD/34258/2006]info:eu-repo/semantics/publishedVersio
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