Paraproducts for bilinear multipliers associated with convex sets

TL;DR

This paper establishes bounds for exotic paraproducts related to bilinear multipliers associated with convex sets, under specific boundary and lacunarity conditions, advancing understanding in harmonic analysis.

Contribution

It introduces new bounds for paraproducts linked to convex set multipliers, considering exponential boundary curves and lacunarity conditions, which are novel in the field.

Findings

Bounds established for paraproducts with exponential boundary curves

Bounds established under higher order lacunarity conditions

Advances in understanding bilinear multipliers associated with convex sets

Abstract

We prove bounds in the local $ L^2 $ range for exotic paraproducts motivated by bilinear multipliers associated with convex sets. One result assumes an exponential boundary curve. Another one assumes a higher order lacunarity condition.