Weighted function spaces and Dunkl transform

2010/05/28 by Abdelkefi, Chokri
#46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 42B10 #Secondary 44A35

paper · doi:10.48550/arxiv.1005.5235

Abstract

We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on Rd weighted Lp-estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L1 when this function belongs to a suitable Besov-Dunkl space.

Related

• Further results for the Dunkl Transform and the generalized Cesàro operator
• Convolution operator and maximal function for Dunkl transform
• Classes of operators on weighted function spaces in Dunkl analysis
• Besov-Dunkl Spaces connected with generalized Taylor formula on the real line
• Harmonic analysis in Dunkl settings