Paraproducts for 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.

v2: authors now in right alphabetical order

References in corpus (3)

• Uniform estimates for some paraproducts
• A sharp estimate for the Hilbert transform along finite order lacunary sets of directions
• On the maximal directional Hilbert transform in three dimensions

Cited by in corpus (1)

• Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity