T. Kopaliani

activity

20132026

most citedLocal Hardy-Littlewood maximal opeator in variable Lebesgue spaces

1 citations · 2 across the 13 of their papers we have counts for

collaborators

14 papers

math.AP2026

Double phase meets Muckenhoupt

Daviti Adamadze, Lars Diening, Tengiz Kopaliani +1

In this paper we generalize the famous result of [FKS] to the double phase model. In particular, we work with minimal assumptions on the modulating coefficient by introducing a Muc…

math.FA2025

Maximal operator on variable exponent spaces

Daviti Adamadze, Lars Diening, Tengiz Kopaliani

We explore the boundedness of the Hardy-Littlewood maximal operator $M$ on variable exponent spaces. Our findings demonstrate that the Muckenhoupt condition, in conjunction with Ne…

math.CA2024

On the embedding between the variable Lebesgue space $L^{p (\cdot)} (Ω)$ and the Orlicz space $L (lo g L)^{α} (Ω)$

David Cruz-Uribe, Amiran Gogatishvili, Tengiz Kopaliani

We give a sharp sufficient condition on the distribution function, $∣ {x \in Ω : p (x) \leq 1 + λ} ∣$ , $λ > 0$ , of the exponent function $p (\cdot) : Ω \to [1, \infty)$ that implies the embed…

math.FA2022

Vilenkin-Fourier series in variable Lebesgue spaces

Daviti Adamadze, Tengiz Kopaliani

Let $S_{n} f$ denote the $n$ th partial sum of the Vilenkin-Fourier series of a function $f \in L^{1} (G)$ . For $1 < p_{-} \leq p_{+} < \infty$ , we characterize all exponents $p(\cdot…

math.FA2020

On singular extensions of continuous functionals from C([0,1]) to variable Lebesgue spaces

Daviti Adamadze, Tengiz Kopaliani

Valadier and Hensgen proved independently that the restriction of functional $ϕ (x) = \int_{0}^{1} x (t) d t, x \in L^{\infty} ([0, 1])$ on the space of continuous functions $C ([0, 1])$ ad…

math.FA2020

divergent Fourier series in function spaces near $L^{1} [0; 1]$

Tengiz Kopaliani, Nino Samashvili, Shalva Zviadadze

In this paper we generalize Bochkariev's theorem, which states that for any uniformly bounded orthonormal system $Φ$ , there exists a Lebesgue integrable function such that the Four…

math.FA2017

Construction of function spaces close to $L^{\infty}$ with associate space close to $L^{1}$

David Edmunds, Amiran Gogatishvili, Tengiz Kopaliani

The paper introduces a variable exponent space $X$ which has in common with $L^{\infty} ([0, 1])$ the property that the space $C ([0, 1])$ of continuous functions on $[0, 1]$ is a close…

math.FA2017

Characterization of interpolation between Grand, small or classical Lebesgue spaces

Aberto Fiorenza, Maria Rosaria Formica, Amiran Gogatishvili +2

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G Γ$ -spaces. As a direct cons…

math.FA2015

Some $s$ -numbers of an integral operator of Hardy type in Banach function spaces

David Edmunds, Amiran Gogatishvili, Tengiz Kopaliani +1

Let $s_{n} (T)$ denote the $n$ th approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator $T$ given by $$ Tf(x)=v(x)\int_{a}^{x}u(t)f(…

math.CA2014

Hardy-Littlewood Maximal Operator And $B L O^{1/ l o g}$ Class of Exponents

Tengiz Kopaliani, Shalva Zviadadze

It is well known that if Hardy-Littlewood maximal operator is bounded in space $L^{p (\cdot)} [0; 1]$ then $1/ p (\cdot) \in B M O^{1/ l o g}$ . On the other hand if $p(\cdot)\in BMO^{1/\log}…

math.FA2014

On the upper and lower estimates of norms in variable exponent spaces

Tengiz Kopaliani, Nino Samashvili, Shalva Zviadadze

In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/ p (\cdot)$ belongs to $BLO^{1…

math.FA2013★ 1 cited

Maximal multiplier operators in $L^{p (\cdot)} (R^{n})$ spaces

Amiran Gogatishvili, Tengiz Kopaliani

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transf…

math.FA2013★ 1 cited

Local Hardy-Littlewood maximal opeator in variable Lebesgue spaces

Ana Danelia, Amiran Gogatishvili, Tengiz Kopaliani

We investigate the class $B^{l oc} (R^{n})$ of exponents $p (\cdot)$ for with local Hardy-Littlewood maximal operator is bounded in $L^{p (\cdot)} (R^{n})$ s…

math.AP2013

Some estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications

Alberto Fiorenza, Amiran Gogatishvili, Tengiz Kopaliani

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for a singular integral operators that are imaginary powers of the Laplace operator in $R^{n}$ . U…