Uniform convergence with rates of general singular operators

• George A Anastassiou ^[1] ; Razvan A Mezei ^[1]
  1. [1] University of Memphis

     University of Memphis

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 2, 2013, págs. 1-20
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000200001
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artí­culo estudiamos propiedades de aproximación de operadores integrales singulares generales sobre la recta real. Establecemos su convergencia al operador unidad con las tasas correspondientes. Las estimaciones son mayormente ajustadas y son tanto puntuales como uniformes. Las desigualdades encontradas involucran el módulo de suavidad de alto orden. Aplicamos esta teorí­a a los operadores singulares trigonométricos.

  • English

    In this article we study the approximation properties of general singular integral operators over the real line. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. We apply this theory to the trigonometric singular operators.

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