On Function Spaces with Fractional Wavelet Transform

Abstract

Let ?1 and ?2 be weight functions on (Formula Presented). In this paper, we define (Formula Presented) to be the vector space of (Formula Presented) such that the fractional wavelet transform (Formula Presented) belongs to (Formula Presented) for 1 ? p, q < ?. We endow this space with a sum norm and show that (Formula Presented) becomes a Banach space. Also we prove that (Formula Presented) is an essential Banach Module over (Formula Presented) under some conditions. We obtain its approximate identities, dual space and multipliers space. At the end of this paper we discuss the inclusion properties, compact embeddings of these spaces. © 2021, MTJPAM Turkey. All rights reserved.