Best possible sufficient conditions for the Fourier transform to satisfy the Lipschitz or Zygmund condition

• Autorzy: Ferenc Móricz
• Języki publikacji: EN

Abstrakty

EN

We consider complex-valued functions f ∈ L¹(ℝ), and prove sufficient conditions in terms of f to ensure that the Fourier transform f̂ belongs to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes zyg(α) and zyg(α) for some 0 < α ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary in the case of real-valued functions f for which either xf(x) ≥ 0 or f(x) ≥ 0 almost everywhere.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 26A16: Lipschitz (H\"older) classes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 2
• Strony: 199-205

Daty

wydano

2010

Twórcy

autor

Ferenc Móricz

• Bolyai Institute University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

Identyfikatory

DOI

10.4064/sm199-2-5