Weighted function spaces and Dunkl transform

Details Weighted function spaces and Dunkl transform Weighted function spaces and Dunkl transform

2010-05-28

arxiv.org/abs/1005.5235v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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.

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