On the classes of functions of bounded partial and total $\Lambda$-variation

A. N. Bakhvalov

On the classes of functions of bounded partial and total $Λ$ -variation

Authors

A. N. Bakhvalov Department of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, 119991, Russia Author

Keywords:

Generalized variation, multiple Fourier series

Subjects:

42B05, 26B30

Abstract

The inclusions of classes of functions with bounded partial $Λ$ -variation into the classes of functions with bounded total harmonic variation are established.The result is applied to the problem of convergence of rectangular partial sums for multiple Fourier series.