Besov-Hankel norms in terms of the Continuous Bessel wavelet transform

TL;DR

This paper extends the continuous Bessel wavelet transform to $L^p$-spaces, derives key formulas, and characterizes Besov-Hankel spaces using wavelet coefficients, advancing the mathematical framework for signal analysis.

Contribution

It introduces an extension of the Bessel wavelet transform to $L^p$-spaces and characterizes Besov-Hankel spaces using wavelet coefficients, providing new analytical tools.

Findings

Derived Parseval's and inversion formulas for the transform

Characterized Besov-Hankel space via wavelet coefficients

Extended Bessel wavelet transform to $L^p$-spaces

Abstract

In this paper, we extend the concept of continuous Bessel wavelet transform in $L^p$-space and derived the Parseval's as well as the inversion formulas. By using Bessel wavelet coefficients we characterized the Besov- Hankel space.