Uniform boundedness of parametric bilinear fractional integrals

TL;DR

This paper establishes uniform weak-type bounds for a family of bilinear fractional integrals related to Euler-Riesz systems, demonstrating sharpness and parameter independence.

Contribution

It introduces sharp, uniform weak-type bounds for parametric bilinear fractional integrals, advancing understanding of their boundedness properties.

Findings

Bounds are uniform across the parameter family.

Bounds are sharp and cannot be extended to larger index sets.

Results apply to bilinear fractional integrals in Euler-Riesz systems.

Abstract

We provide weak-type bounds for a family of bilinear fractional integrals that arise in the study of Euler-Riesz systems. These bounds are uniform in the natural parameter that describes the family and are sharp, in the sense that they do not hold for any larger set of indices.