Boundedness of Bilinear Bessel Potentials

TL;DR

This paper introduces bilinear Bessel potentials, analyzes their boundedness properties between various function spaces, and identifies optimal Lorentz space indices through explicit counterexamples.

Contribution

It is the first to define bilinear Bessel potentials and thoroughly characterize their boundedness, including optimal Lorentz space indices.

Findings

Bilinear Bessel potentials are bounded from L^p × L^q into Lebesgue and Lorentz spaces.

Optimal Lorentz indices are identified via explicit counterexamples.

The results extend the understanding of bilinear potential operators in harmonic analysis.

Abstract

In analogy with bilinear Riesz potentials, we introduce bilinear Bessel potentials and characterize their boundedness from $L^p\times L^q$ into Lebesgue and Lorentz spaces $L^{r,\alpha}.$ In several cases we identify the optimal Lorentz indices by constructing explicit counterexamples.