Convolution functions of several variables with generalized bounded variation

Let L ¹ be the class of all complex-valued functions, with period 2π in each variable, in the space , where $\mathbb{T} = [0,2\pi )$ is the one-dimensional torus. Here, it is observed that L ¹ * E ? E for E = Lip(p; α ₁, α ₂, ..., α _N ) over , for , for , and for in the sense of Vitali as well as Hardy.     

Summability of multiple Fourier series of functions of bounded generalized variation

The paper is devoted to summability problems for multiple Fourier series of functions of bounded generalized variation. We find necessary and sufficient conditions on a sequence Λ = {λ _n } that guarantee the convergence of the Cesàro means of multiple Fourier series of functions of bounded Λ-variation.     

A note on Lagrange interpolation of functions of generalized bounded variation

In this paper we solve a remained problem in [2], whether the following estimate approximation for the classf∈[-1, 1]∩BV by Lagrange interpolation based on the Jacobi abscissas: L _n ^(a,d) (f,x)−f(x)=O(1/n) holds, if α≠β α,β≥−1. The project is supported by the Natural Science Foundation of Zhejiang Province.     

Convergence of two-dimensional trigonometric interpolation polynomials of functions of bounded harmonic variation

The paper considers a question of convergence of partial sums of two-dimensional trigonometric interpolation polynomials. Convergence by Pringsheim for functions of two variables with bounded harmonic variation is established.     

The exact correction theorem for spaces of functions of generalized bounded variation

Mathematical Notes -     

On the convergence of multiple Walsh-Fourier series of functions of bounded generalized variation

The convergence of multiple Walsh-Fourier series of functions of bounded generalized variation is investigated. The sufficient and necessary conditions on the sequence ?? = {?? _n } are found for the convergence of multiple Walsh-Fourier series of functions of bounded partial ??-variation.     

Conditions for the existence of stieltjes integral of functions of bounded generalized variation

, , , , - , , , , . . . .     

Convergence of double fourier series for functions of bounded generalized variation. II

Siberian Mathematical Journal -     

Embedding of classes of functions with bounded {\Phi}-variation into generalized Lipschitz spaces

In this note, sufficient and necessary conditions for embedding of classes \({\Phi}\)BV of functions with bounded \({\Phi}\)-variation in Schramm’s sense into generalized Lipschitz classes \({H_{q}^{\omega} (1 \leq q < \infty)}\) are obtained.     

On the convergence of multiple Fourier series of functions of bounded partial generalized variation

The convergence of multiple Fourier series of functions of bounded partial Λ-variation is investigated. The sufficient and necessary conditions on the sequence Λ = {λ _n } are found for the convergence of multiple Fourier series of functions of bounded partial Λ-variation.     

Gap series and functions of bounded variation

Summary We prove that the gap seriesΣf(n _k x) does not behave like an independent random series when f is a function of bounded variation with rational discontinuity.     

Convergence of double Fourier series for functions of bounded generalized variation. Pt. 1

Siberian Mathematical Journal -     

Traces of functions of generalized Sobolev classes

Considering the Sobolev type function classes on a metric space equipped with a Borel measure we address the question of compactness of embeddings of the space of traces into Lebesgue spaces on the sets of less “dimension.” Also, we obtain compactness conditions for embeddings of the traces of the classical Sobolev spaces W _p ¹ on the “zero” cusp with a Hölder singularity at the vertex.     

Factorization of functions in generalized Nevanlinna classes

For functions in the classical Nevanlinna class analytic projection of produces where is the outer part of i.e., this projection factors out the inner part of . We show that if is area integrable with respect to certain measures on the disc, then the appropriate analytic projections of factor out zeros by dividing by a natural product which is a disc analogue of the classical Weierstrass product. This result is actually a corollary of a more general theorem of M. Andersson. Our contribution is to give a simple one complex variable proof which accentuates the connection with the Weierstrass product and other canonical objects of complex analysis.