# Boas' problem for Hankel transforms

## TL;DR

This paper investigates norm equivalences between functions and their Hankel transforms within weighted Lebesgue and Lorentz spaces, extending Boas'-type results to real-valued monotone functions and also providing analogous Fourier transform results.

## Contribution

It introduces new Boas'-type theorems for Hankel transforms involving real-valued monotone functions in weighted and Lorentz spaces, expanding existing Fourier analysis literature.

## Key findings

- Established norm equivalences in weighted Lebesgue spaces
- Extended Boas'-type results to Lorentz spaces
- Provided analogous results for Fourier transforms

## Abstract

Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas'-type results involving real-valued general monotone functions are obtained. Corresponding results for the Fourier transform are also given.