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The T1 theorem for the Hilbert transform fails when p is not 2

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer, Ignacio Uriarte-Tuero

Abstract

Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2

The T1 theorem for the Hilbert transform fails when p is not 2

Abstract

Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2
Paper Structure (3 sections, 20 equations)

This paper contains 3 sections, 20 equations.

Table of Contents

  1. Introduction
  2. Cantor construction
  3. Failure of $\mathcal{A}_{p}^{\ell^{2}}\left( \sigma ,\omega\right)$

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3