Daviti Adamadze

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20202026

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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…