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Generalized weighted Besov spaces on the Gegenbauer hypergroup

Ibrahimov E. J.

Commentationes Mathematicae

2014

Vol 54, No. 1

95--128

In this paper we study generalized weighted Besov type spaces on the Gegenbauer hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces. Obtained results are analogies of the results for generalized Bessel shifts obtained in the work [5].