Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
-
Seymur S. Aliev
und
Vagif S. Guliev
Abstract.
In this paper we study the boundedness of the parametric Marcinkiewicz operator
on generalized Morrey spaces 
.
We find the sufficient conditions on the pair 
which
ensure the boundedness of the operators from one generalized
Morrey space 
to another 
,
, and from the space 
to the weak space 
.
As an application of the above result, the boundedness
of the commutator of Marcinkiewicz operators 
on generalized Morrey spaces is also obtained.
In the case 
, we find the sufficient conditions on the pair which
ensure the boundedness of the operators from one generalized
Morrey space to another ,
, and from the space to the weak space .
In all the cases the conditions for boundedness are given in terms of Zygmund-type integral inequalities on
which do not require any assumption on the
monotonicity of 
.
© 2012 by Walter de Gruyter Berlin Boston
Artikel in diesem Heft
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
Artikel in diesem Heft
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
