Andrei K. Lerner

collaborators

5 papers

math.CA2026

Failure of the linear $A_{2}$ bound for the strong maximal operator

Andrei K. Lerner

We show that the strong maximal operator on $R^{2}$ does not satisfy a linear weighted $L^{2}$ estimate in terms of the rectangular $A_{2}$ characteristic. More precisely, we c…

math.CA2026

Dual boundedness of the maximal operator on concave Banach function spaces

Andrei K. Lerner

We prove a conjecture of Nieraeth asserting that if the Hardy--Littlewood maximal operator $M$ is bounded on an $s$ -concave Banach function space $X$ for some $s \in (1, \infty)$ , th…

math.CA2026

Sparse domination of Calderón-Zygmund operators by mean oscillations

Andrei K. Lerner

We show that if $T$ is a Dini-continuous Calderón--Zygmund operator satisfying $T (1) = 0$ , then the usual sparse domination for $T$ can be sharpened by replacing local averages with…

math.CA2026

The maximal operator on variable Lebesgue spaces: an $A_{\infty}$ -characterization

Andrei K. Lerner

In this paper we obtain a new boundedness criterion for the maximal operator $M$ on variable exponent spaces $L^{p (\cdot)}$ . It is formulated in terms of the variable exponent anal…

math.CA2024

A note on the maximal operator on Banach function spaces

Andrei K. Lerner

In this note we answer positively to two conjectures proposed by Nieraeth (2023) about the maximal operator on rescaled Banach function spaces. We also obtain a new criterion sayin…

Failure of the linear A2​ bound for the strong maximal operator

Dual boundedness of the maximal operator on concave Banach function spaces

Sparse domination of Calderón-Zygmund operators by mean oscillations

The maximal operator on variable Lebesgue spaces: an A∞​-characterization

A note on the maximal operator on Banach function spaces

Failure of the linear $A_{2}$ bound for the strong maximal operator

The maximal operator on variable Lebesgue spaces: an $A_{\infty}$ -characterization