A characterization of weighted Besov spaces in quantum calculus

Abstract

In this paper, subspaces of L p (Rq,+) are defined using q-translations Tq,x operator and qdifferences operator, called q-Besov spaces. We provide characterization of these spaces by using the q-convolution product.

Calderón’s reproducing Formula For q-Bessel operator

“…Calderón's formula [1] involving convolutions related to the Fourier transform is useful in obtaining reconstruction formula for wavelet transform, in decomposition of certain spaces and in characterization of Besov spaces [6,8,10]. Calderón's reproducing formula was also established for Bessel operator [4,5].…”