The Fourier-Walsh series of the functions absolutely continuous in the generalized restricted

• Autores: S. F. Lukomskii
• Localización: Siberian mathematical journal, ISSN 0037-4466, Vol. 48, Nº. 2, 2007, págs. 273-282
• Idioma: inglés
• DOI: 10.1007/s11202-007-0027-z
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• Resumen

  • We consider the questions of convergence in Lorentz spaces for the Fourier-Walsh series of the functions with Denjoy integrable derivative. We prove that a condition on a function f sufficient for its Fourier-Walsh series to converge in the Lorentz spaces "near" L cannot be expressed in terms of the growth of the derivative f'.