**Title:** On Function Spaces with Fractional Wavelet Transform

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-20-00045; **Volume 3 / Issue 3 / Year 2021 (Special Issue)**, Pages 122-134

**Document Type:** Research Paper

**Author(s):** Muhammed Duman ^{a} , Öznur Kulak ^{b}

^{a}Giresun University, Faculty of Sciences and Letters, Department of Mathematics, Giresun, Turkey

^{b}Amasya University, Faculty of Sciences and Letters, Department of Mathematics, Amasya, Turkey

Received: 5 December 2020, Accepted: 1 January 2021, Published: 25 April 2021.

**Corresponding Author:** Öznur Kulak (Email address: oznur.kulak@amasya.edu.tr)

**Full Text:** PDF

**Abstract**

Let and be weight functions on . In this paper, we define to be the vector space of such that the fractional wavelet transform belongs to for 1 ≤ *p*, *q* < ∞.
We endow this space with a sum norm and show that becomes a Banach space. Also we prove that is an essential Banach Module over 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.

**Keywords:** Fractional wavelet transform, Essential Banach module, Approximate identity, Compact embedding, Multipliers space

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