Lebesgue points and convergence over cone-like sets

• Ferenc Weisz ^[1]
  1. [1] Eötvös L. University
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 9, Nº. 1-2, 2017, págs. 65-83
• Idioma: inglés
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• Resumen

  • We generalize the well known Lebesgue’s theorem about the convergence of Fejér means for higher dimensions. Under some conditions on θ, we show that the summability means σθT f of a function f from the largest Wiener amalgam space W(L1 (Rd) converge to f at each modified Lebesgue point, whenever T → ∞ and T is in a cone-like set. The result holds for the Weierstrass, Abel, Picar, Bessel, Fejér, Cesàro, de La Vallée-Poussin, Rogosinski and Riesz summations.