Continuous Bessel wavelet transform of distributions

Santosh Kumar Upadhyay; Jay Singh Maurya

doi:10.1216/rmj-2021-51-1463

Abstract

The continuous Bessel wavelet transform is extended to distributions in $H_\mu ^{^\prime }\left( {0,\infty } \right)$ and obtained continuity results. Boundedness of continuous Bessel wavelet transform is investigated in a generalized Sobolev space, Besov space and Triebel–Lizorkin space.

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Santosh Kumar Upadhyay. Jay Singh Maurya. "Continuous Bessel wavelet transform of distributions." Rocky Mountain J. Math. 51 (4) 1463 - 1488, August 2021. https://doi.org/10.1216/rmj.2021.51.1463

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Received: 13 February 2020; Accepted: 10 November 2020; Published: August 2021

First available in Project Euclid: 5 August 2021

MathSciNet: MR4298860

zbMATH: 1483.46041

Digital Object Identifier: 10.1216/rmj.2021.51.1463

Subjects:

Primary: 46F05 , 46F12

Secondary: 44A35 , 65T60

Keywords: Besov space and Triebel–Lizorkin space , continuous Bessel wavelet transform , Hankel transform , Sobolev space , Zemanian space and its dual

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