$H^1$ to $L^q$-boundedness of fractional integral operators having a flag kernel

TL;DR

This paper characterizes when certain fractional integral operators with non-isotropic kernels are bounded from the Hardy space to L^q spaces, expanding understanding of their behavior in harmonic analysis.

Contribution

It provides a new characterization of boundedness for fractional integral operators with flag kernels from H^1 to L^q spaces.

Findings

Operators are bounded from H^1 to L^q under specific kernel conditions

Characterization involves non-isotropic dilation properties

Results extend classical boundedness criteria to flag kernels.

Abstract

We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable $H^1$-Hardy space to $L^q$-spaces.