Boundedness of multidimensional Hausdorff operators on $L^1$ and $H^1$ spaces

TL;DR

This paper establishes new boundedness conditions for a broad class of multivariate Hausdorff operators on the real Hardy space $H^1$, utilizing atomic decomposition techniques.

Contribution

It introduces a novel, stronger boundedness criterion for multivariate Hausdorff operators on $H^1$, expanding understanding of their behavior in harmonic analysis.

Findings

Derived a new boundedness condition for Hausdorff operators on $H^1$

Applied atomic decomposition to prove boundedness

Extended results to a wide family of multivariate operators

Abstract

For a wide family of multivariate Hausdorff operators, a new stronger condition for the boundedness of an operator from this family on the real Hardy space $H^1$ by means of atomic decomposition.