Work

Titchmarsh theorems on Damek–Ricci spaces via moduli of continuity of higher order

Year: 2024

Type: article

Abstract: A classical theorem of Titchmarsh relates the [Formula: see text]-Lipschitz functions and decay of the Fourier transform of the functions. In this note, we prove the Titchmarsh theorem for Damek–Ricci space (also known as harmonic [Formula: see text] groups) via moduli of continuity of higher orders. We also prove an analogue of another Titchmarsh theorem which provides integrability properties of the Fourier transform for functions in the Hölder Lipschitz spaces.

Source: International Journal of Mathematics

DOI: 10.1142/s0129167x25500016

Authors: Manoj Kumar, Vishvesh Kumar, Michael Ruzhansky

Institutions: Indian Institute of Science Bangalore, Ghent University, Queen Mary University of London

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green