Abstract
The convergence of multiple Fourier series of functions of bounded partial Λ-variation is investigated. The sufficient and necessary conditions on the sequence Λ = {λn} are found for the convergence of multiple Fourier series of functions of bounded partial Λ-variation.
Highlights
We say that the function f has Bounded Partial Λ1, ..., Λd variation and write f ∈ P BVΛ1,...,Λd if d
The notion of bounded partial variation was introduced by Goginava in [6, 7]. These classes of functions of generalized bounded variation play an important role in the theory Fourier series
< ∞, Using the third statement of Theorem A, we have proved in [8] the convergence of double Fourier series of functions of any class P BVΛ with (2)
Summary
The Λj1, ..., Λjp -variation of f with respect to index set α is defined as follows: VΛαj1 ,...,Λjp (f ) We say that the function f has total Bounded Λ1, ..., Λd variation on T d = [0, 2π]d and write f ∈ BVΛ1,...,Λd, if We say that the function f has Bounded Partial Λ1, ..., Λd variation and write f ∈ P BVΛ1,...,Λd if d
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