Nazerke Tleukhanova

A Lizorkin Theorem on Fourier Series Multipliers for Strong Regular Systems

A new Fourier series multiplier theorem of Lizorkin type is proved for the case 1<q<p<∞.The result is given for a general strong regular system and, in particular, for the trigonometric system it implies an analogy of the original Lizorkin theorem.

The multipliers of multiple trigonometric Fourier series

Abstract We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.

On multipliers of Fourier series in the Lorentz space

We study the multipliers of Fourier series on the Lorentz spaces, in particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Z in order to make it a multiplier of trigonometric Fourier series of space Lp,r [0; 1] in the Lq,r [0; 1]. In the paper there is a new multipliers theorem which is supplement of the well-known theorems, and given a counterexample.

The Marcinkiewicz Theorem on the Multipliers of Fourier Series for Weighted Lebesgue Spaces

This paper is devoted to the study of Fourier series multipliers . An analog of the Marcinkiewicz theorem on multipliers of Fourier series in weighted Lebesgue spaces is obtained.

Some New Fourier Multiplier Results of Lizorkin and Hörmander Types

This paper is devoted to the study of Fourier series and Fourier transform multipliers and contains introduction, which put some new results into a general frame. In the following Sections several further examples and results are presented and discussed. In Section 2 we present some important results (including the most early papers we know) concerning Fourier series multipliers of particular interest for the investigations. The corresponding result for Fourier transform multipliers can be found in Section 3. In Section 4 we give some applications and in Section 5 we describe shortly the main results: A generalization and sharpening of the Lizorkin theorem concerning Fourier transform multipliers between \(L_p\) and \(L_q\). The Fourier series multipliers in the case with a regular system, which is rather general. A generalization and sharpening of the Lizorkin type theorem concerning Fourier series multipliers between \(L_p\) and \(L_q\) in this general case. A generalization of the Hormander multiplier theorem for two dimensional Fourier series to the case with a general regular system .

Summability of the Fourier coefficients of functions from anisotropic Lorentz space

In this paper the generalization of the Hardy-Littlewood-Polya inequality and Nursultanov inequality is proved.