Characterization of weighted function spaces in terms of wavelet transforms

Abstract

In this paper, we have characterized a weighted function space $ B_{\omega,\psi}^{p,q}, ~ 1\leq p,q<\infty$ in terms of wavelet transform and shown that the norms on the spaces $B_{\omega,\psi}^{p,q}$  and $\bigwedge_\omega^{p,q}$ (the space defined in terms of differences $\triangle_x$) are equivalent.