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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 47: Issue 1
DOI:
https://doi.org/10.1556/sscmath.2009.1109
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 (
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) where 1 < p ≦ q < ∞ 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 f ∈ L w p (
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) has been estimated in the case p = q and υ ≡ w . The generalized Bernstein inequality applied to estimate the order of best trigonometric approximation of the derivative of functions f ∈ L w p (
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) in the space L υ q (
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).
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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 51: Issue 3
DOI:
https://doi.org/10.1556/sscmath.51.2014.3.1290
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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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 56: Issue 2
DOI:
https://doi.org/10.1556/012.2019.56.2.1425
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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