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
aGiresun University, Faculty of Sciences and Letters, Department of Mathematics, Giresun, Turkey
bAmasya 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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