Besov-type spaces for the Dunkl operator on the real line
نویسندگان
چکیده
منابع مشابه
Characterization of Besov Spaces for the Dunkl Operator on the Real Line
In this paper, we define subspaces of L by differences using the Dunkl translation operators that we call Besov-Dunkl spaces. We provide characterization of these spaces by the Dunkl convolution.
متن کاملBesov–dunkl Spaces Connected with Generalized Taylor Formula on the Real Line
In the present paper, we define for the Dunkl tranlation operators on the real line, the Besov–Dunkl space of functions for which the remainder in the generalized Taylor’s formula has a given order. We provide characterization of these spaces by the Dunkl convolution.
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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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In this paper, we show the inclusion and the density of the Schwartz space in Besov–Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov–Dunkl space.
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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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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.06.054