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BESOVTYPE SPACES ON Rd AND INTEGRABILITY FOR THE DUNKL TRANSFORM
 

Summary: BESOV­TYPE SPACES ON Rd
AND INTEGRABILITY FOR THE DUNKL TRANSFORM
CHOKRI ABDELKEFI
, JEAN-PHILIPPE ANKER
, FERIEL SASSI
& MOHAMED SIFI §
Abstract. In this paper, we show the inclusion and the density of the Schwartz space
in Besov­Dunkl 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 Besov­Dunkl space.
1. Introduction
We consider the differential-difference operators Ti, 1 i d, on Rd
, associated with
a positive root system R+ and a non negative multiplicity function k, introduced by
C.F. Dunkl in [9] and called Dunkl operators (see next section). These operators can be
regarded as a generalization of partial derivatives and lead to generalizations of various
analytic structure, like the exponential function, the Fourier transform, the translation
operators and the convolution (see [8, 10, 11, 16, 17, 18, 19, 22]). The Dunkl kernel Ek has
been introduced by C.F. Dunkl in [10]. This kernel is used to define the Dunkl transform

  

Source: Anker, Jean-Philippe - Laboratoire de Mathématiques et Applications, Physique Mathématique, Université d'Orléans

 

Collections: Mathematics