M. G. Magomed-Kasumov, “Convergence of Fourier–Haar Rectangular Sums in Lebesgue Spaces with Variable Exponent <nobr>$L^{p(x,y)}$</nobr>”, Izv. Saratov Univ. Math. Mech. Inform., 2013, Volume 13, Issue 1(2),Pages <nobr>76

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Mathematics

Convergence of Fourier–Haar Rectangular Sums in Lebesgue Spaces with Variable Exponent $L^{p(x,y)}$

M. G. Magomed-Kasumov

South Mathematical Institute of VSC RAS

Abstract: Convergence of Fourier–Haar rectangular partial sums in Lebesgue spaces with variable exponent is proved in this paper.

Key words: two-dimensional Haar system, Lebesgue spaces with variable exponent, Dini–Lipschitz condition, convergence, rectangular partial sums.

UDC: 517.51

DOI: 10.18500/1816-9791-2013-13-1-2-76-81