Rearrangement estimates for fourier transforms in Lp and Hp in terms of moduli of continuity

  1. García-Cuerva, J. 2
  2. Kolyada, V.I. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Autónoma de Madrid
    info

    Universidad Autónoma de Madrid

    Madrid, España

    ROR https://ror.org/01cby8j38

Revista:
Mathematische Nachrichten

ISSN: 0025-584X

Any de publicació: 2001

Volum: 228

Pàgines: 123-144

Tipus: Article

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DOI: 10.1002/1522-2616(200108)228:1<123::AID-MANA123>3.0.CO;2-A SCOPUS: 2-s2.0-18344410920 WoS: WOS:000170870600005 GOOGLE SCHOLAR

Altres publicacions en: Mathematische Nachrichten

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Resum

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 &lt; p ≤ 1, n ∈ ℕ).