Pointwise Behavior of Double Fourier Series of Functions of Bounded Variation

• Autores: Ferenc Móricz
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 148, Nº 1, 2006, págs. 51-59
• Idioma: inglés
• DOI: 10.1007/s00605-005-0347-7
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• Resumen

  • We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries, we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version.