Daviti Adamadze

activity

20202026

collaborators

5 papers

math.AP2026

Variable Exponent Regularity via Muckenhoupt Condition

Daviti Adamadze, Anna Kh. Balci, Lars Diening

For the first time, we establish higher integrability of the gradient and local $L^{\infty}$ estimates of weak solutions to the $p (x)$ -Laplacian without assuming $lo g$ -Hölder contin…

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.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…