Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

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Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

and Applied Analysis 3 For all x, y, z ∈ R, we put Wα ( x, y, z ) : ( 1 − σx,y,z σz,x,y σz,y,x ) Δα ( x, y, z ) , 2.5

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Boundedness of the Fractional Maximal Operator in Local Morrey-type Spaces

The problem of the boundedness of the fractional maximal operator Mα, 0 ≤ α < n in local Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters.

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Dunkl Translation and Uncentered Maximal Operator on the Real Line

On the real line, the Dunkl operators are differential-difference operators introduced in 1989 by Dunkl [1] and are denoted by Λα, where α is a real parameter > −1/2. These operators are associated with the reflection group Z2 on R. The Dunkl kernel Eα is used to define the Dunkl transform α which was introduced by Dunkl in [2]. Rösler in [3] shows that the Dunkl kernels verify a product formul...

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ژورنال

عنوان ژورنال: Abstract and Applied Analysis

سال: 2010

ISSN: 1085-3375,1687-0409

DOI: 10.1155/2010/976493