Rearrangement estimates for fourier transforms in Lp and Hp in terms of moduli of continuity
- García-Cuerva, J. 2
- Kolyada, V.I. 1
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1
Universidad de La Rioja
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2
Universidad Autónoma de Madrid
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ISSN: 0025-584X
Ano de publicación: 2001
Volume: 228
Páxinas: 123-144
Tipo: Artigo
beta Ver similares en nube de resultadosOutras publicacións en: Mathematische Nachrichten
Resumo
One of the main purposes of this paper is to obtain estimates for Fourier transforms of functions in Lp(ℝn) (1 ≤ p ≤ 2) in terms of their moduli of continuity. More precisely, we study the following problem: find sharp conditions on the modulus of continuity of a function f ∈ Lp(ℝn), under which the non-increasing rearragement of f̂, the Fourier transform of f, is integrable against a given non-negative weight function ρ. We shall also study similar problems for the Fourier transforms of functions or distributions in the Hardy spaces Hp(ℝn) (0 < p ≤ 1, n ∈ ℕ).