ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# мультипликативная система

## Necessary and sufficient conditions of belonging to the Besov–Potapov classes and Fourier coefficients with respect to multiplicative systems

In this paper we obtain necessary and sufficient conditions for a function to belong to the Besov–Potapov classes. Using functions with Fourier coefficients with respect to multiplicative systems from the class GM, we show the sharpness of some these results.

## Weighted Integrability of Sums of Series with Respect to Multiplicative Systems

A necessary and sufficient condition for Lp-integrability with power weight of a function f represented by the series with respect to multiplicative systems with generalized monotone coefficients is obtained. The integrability of the majorant of partial sums of a representing series is also described by the same conditions. In addition we study the integrability of difference quotient (f(x) − f(0))/x.

## Uniform Convergence of the Series with Respect to Multiplicative Systems

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