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• Author or Editor: Vakhtang Kokilashvili
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## Two-weight estimates for Fourier operators and Bernstein inequality

Studia Scientiarum Mathematicarum Hungarica
Authors:
Ali Guven
and
Vakhtang Kokilashvili
The norm estimation problem for Fourier operators acting from L w p (
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) to L υ q (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
) where 1 < pq < ∞ was investigated. These results has been generalized to the two-dimensional case and applied to obtain generalizations of the Bernstein inequality for trigonometric polynomials of one and two variables. Also, the rates of convergence of Cesaro and Abel-Poisson means of functions fL w p (
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) has been estimated in the case p = q and υw . The generalized Bernstein inequality applied to estimate the order of best trigonometric approximation of the derivative of functions fL w p (
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) in the space L υ q (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{T}$$ \end{document}
).
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## Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces

Studia Scientiarum Mathematicarum Hungarica
Authors:
Vakhtang Kokilashvili
and
Alexander Meskhi

Two-weight norm estimates for sublinear integral operators involving Hardy-Littlewood maximal, Calderón-Zygmund and fractional integral operators in variable exponent Lebesgue spaces are derived. Operators and the space are defined on a quasi-metric measure space with doubling condition. The derived conditions are written in terms of L p(·) norms and are simultaneously necessary and sufficient for appropriate inequalities for maximal and fractional integral operators mainly in the case when weights are of radial type.

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## Commutators of sublinear operators in grand morrey spaces

Studia Scientiarum Mathematicarum Hungarica
Authors:
Vakhtang Kokilashvili
,
Alexander Meskhi
, and
Humberto Rafeiro

## Abstract

In this paper we establish the boundedness of commutators of sublinear operators in weighted grand Morrey spaces. The sublinear operators under consideration contain integral operators such as Hardy-Littlewood and fractional maximal operators, Calderón-Zygmund operators, potential operators etc. The operators and spaces are defined on quasi-metric measure spaces with doubling measure.

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