ON \(\Lambda\)-CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES

Nikolai Yu. Antonov     (Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation)

Abstract


We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the \(\lambda \)-convergence for \(\lambda >1\). The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class \( L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d ) \) has been generalized to the case of the \( \Lambda \)-convergence for some sequences \(\Lambda\).


Keywords


Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere

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DOI: http://dx.doi.org/10.15826/umj.2017.2.003

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