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On grand Lorentz spaces and the maximal operator
-
Pankaj Jain
und
Santosh Kumari
Veröffentlicht/Copyright:
30. Mai 2012
Abstract.
The notion of the classical Lorentz space 
is generalized to the grand Lorentz space 
. Some basic properties of the space are proved and
the boundedness of the maximal operator M is characterized in
. It is shown that 
is bounded if and only if the weight w belongs to the famous 
-class.
Keywords: Lorentz space; grand Lorentz space; grand Lebesgue space; maximal operator; averaging operator; -class
Received: 2011-07-01
Revised: 2012-01-31
Published Online: 2012-05-30
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Schlagwörter für diesen Artikel
Lorentz space;
grand Lorentz space;
grand Lebesgue space;
maximal operator;
averaging operator;
-class
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
