Decay of Fourier Transforms and Generalized Besov Spaces

Jordão, Thaís

doi:10.33205/cma.646557

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…In terms of the moduli of continuity, the theorem has been explored on R [30,13] and the rank one symmetric spaces [16]. See [6,17,18] for some growth properties of the Fourier transform on certain spaces via moduli of continuity.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar¹,

Kumar²,

Ruzhansky³

2022

Preprint

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A classical theorem of Titchmarsh relates the L 2 -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 N A 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.

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Section: Introductionmentioning

confidence: 99%

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

Kumar¹,

Kumar²,

Ruzhansky³

2022

Preprint

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“…Other studies of Lipschitz conditions have been done in [22,23,24,25] in term of the modulus of continuity. However, our aim in this paper is to extend the classical Titchmarsh theorems in case of functions of the wider Lipschitz class in the space L 2 (R d , w l (x)dx) in terms of the moduli of continuity of higher orders.…”

Section: Introductionmentioning

confidence: 99%

Generalized Lipschitz and Besov spaces in terms of decay of Dunkl transforms in the space L2(Rd, wl(x)dx)

Ouadih

Daher²

2022

Preprint

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Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform

Mannai,

Negzaoui

2024

Analysis

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The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {\kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(\kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {\mathcal{F}_{\kappa,n}} .

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Decay of Fourier Transforms and Generalized Besov Spaces

Cited by 5 publications

References 29 publications

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

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

Generalized Lipschitz and Besov spaces in terms of decay of Dunkl transforms in the space L2(Rd, wl(x)dx)

Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform

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