равномерная сходимость

On the Representation of Functions by Absolutely Convergent Series by H -system

Authors: Navasardyan K. A.

The paper deals with the representation of absolutely convergent series of functions in spaces of homogeneous type. The definition of a system of Haar type (H-system) associated to a dyadic family on a space of homogeneous type X is given in the Introduction. It is proved that for almost everywhere (a.e.) finite and measurable on a set  X  function f there exists an absolutely convergent series by the system H, which converges to  f  a.e. on  X .

Λ-Summability and Multiplicators of Holder Classes of Fourierseries with Respect ̈ to Character Systems

Authors: Agafonova N. Y.

Let G be a Vilenkin group of bounded type. We obtain nessesary and sufficient conditions of uniform Λ-summability for all Fourier series of f ∈ C(G) and one of Λ-summability in L 1 (G) for all Fourier series of f ∈ L 1 (G). Also we extend some T. Quek and L. Yap results to the case of general modulus of continuity.

On Uniform Convergenceof Transformationsof Fourier Serieson Multiplicative Systems

Authors: Agafonova N. Y.

Necessary and suffiecient conditions for uniform Λ-summability of Fourier – Vilenkin series of Functions from Orlicz spaces LΦ[0,1) and L1[0,1) are obtained. Some corollaries for matrices with generalized monotone coeffiecients are given.

Necessary and Sufficient Conditions for the Uniform on a Segment Sinc-approximations Functions of Bounded Variation

Authors: Trynin A. Y.

The necessary and sufficient conditions for the uniform convergence of sinc-approximations of functions of bounded variation is obtained. Separately we consider the conditions for the uniform convergence in the interval (0, π) and on the interval [0, π]. The impossibility of uniform approximation of arbitrary continuous function of bounded variation on the interval [0, π] is settled.

Uniform Convergence of the Series with Respect to Multiplicative Systems

Authors: Fadeev R. N.

Two theorems on uniform convergence and boundedness of partial sums for the series with generalized monotone coefficients with respect to multiplicative systems are proved.

Embedding Theorems for P-nary Hardy and VMO Spaces

Authors: Volosivets S. S.

In the present paper several embedding theorems of P. L. Ul’yanov type for H¨older spaces connected with P-nary Hardy, VMO, L1 and uniform metric on Vilenkin groups are proved. Its sharpness is also established. The sufficient conditions for the convergence of Fourier series with respect to multiplicative systems in Hardy space and uniform metric are also given.