The sets of convergence in measure of multiple orthogonal Fourier series

• Autores: Rostom Getsadze
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 1, 2005, págs. 239-257
• Idioma: inglés
• DOI: 10.1112/s0024610705006678
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• Resumen

  • Let be an arbitrary orthonormal system on [0,1] that is uniformly bounded by a constant . Let be a subset of [0,1] such that the Fourier series of all Lebesgue integrable functions on [0,1] with respect to the product system converge in measure by squares on . The following problem is studied. How large may the measure of be? A theorem is proved that implies that for each such system, there is (for the -fold product systems, ). This estimate is sharp in the class of all such product systems.