ON \(\Lambda\)-CONVERGENCEALMOST EVERYWHEREOF MULTIPLE TRIGONOMETRIC FOURIERSERIES

Ural Mathematical Journal

Nikolai Yu. Antonov¹ 

[1] Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg;

关键词: Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere;   

DOI  :  10.15826/umj.2017.2.003

来源: DOAJ

【 摘 要 】

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 \(\Lambda\).

【 授权许可】

Unknown