A. Shalukhina

activity

20182025

collaborators

4 papers

math.CA2025

The maximal function on spaces of homogeneous type, or adjacent dyadic cubes do good

Alina Shalukhina

We prove that the Hardy--Littlewood maximal operator $M$ is bounded on the variable Lebesgue space $L^{p (\cdot)} (X, d, μ)$ , with $1 < p_{-} \leq p_{+} < \infty$ , over an unbounded space of hom…

math.CA2024

Self-improving boundedness of the maximal operator on quasi-Banach lattices over spaces of homogeneous type

Alina Shalukhina

We prove the self-improvement property of the Hardy--Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our…

math.FA2024

A necessary condition for the boundedness of the maximal operator on $L^{p (\cdot)}$ over reverse doubling spaces of homogeneous type

Oleksiy Karlovych, Alina Shalukhina

Let $(X, d, μ)$ be a space of homogeneous type and $p (\cdot) : X \to [1, \infty]$ be a variable exponent. We show that if the measure $μ$ is Borel-semiregular and reverse doubling, then t…

math.CA2018

On the extension of the Reverse Hölder Inequality for power functions on the real axis

Alina Shalukhina

We consider the class of all non-negative on $R_{+}$ functions such that each of them satisfies the Reverse Hölder Inequality uniformly over all intervals with some constant…

The maximal function on spaces of homogeneous type, or adjacent dyadic cubes do good

Self-improving boundedness of the maximal operator on quasi-Banach lattices over spaces of homogeneous type

A necessary condition for the boundedness of the maximal operator on Lp(⋅) over reverse doubling spaces of homogeneous type

On the extension of the Reverse Hölder Inequality for power functions on the real axis

A necessary condition for the boundedness of the maximal operator on $L^{p (\cdot)}$ over reverse doubling spaces of homogeneous type