Generalized weighted Besov spaces on the Gegenbauer hypergroup

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].