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Paraproducts for bilinear multipliers associated with convex sets

Olli Saari, Christoph Thiele

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.

Paraproducts for bilinear multipliers associated with convex sets

Abstract

We prove bounds in the local 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.

Paper Structure

This paper contains 3 sections, 14 theorems, 102 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['exppara']}
  3. Multi-lacunary paraproducts

Key Result

Theorem 1.1

Let $p_1,p_2,p_3$ be as in locall2. Define Then the operator bilmult satisfies the a priori estimate holder.

Theorems & Definitions (24)

  • Theorem 1.1
  • Corollary 1.2
  • Definition 1.3: Multi-lacunarity
  • Theorem 1.4
  • Lemma 2.1
  • proof
  • Theorem 2.2
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • ...and 14 more