Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Good Lambda Inequalities and Variable Orlicz Hardy Spaces

Timothy Ferguson

Abstract

We prove a general theorem showing that local good-$λ$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.

Good Lambda Inequalities and Variable Orlicz Hardy Spaces

Abstract

We prove a general theorem showing that local good- inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.

Paper Structure

This paper contains 9 sections, 14 theorems, 109 equations.

Table of Contents

  1. Introduction
  2. Hardy Spaces
  3. Uneven Layer Cake Decomposition
  4. An Application to Harmonic Functions
  5. The Jensen property
  6. Maximal Functions and the Jensen Property
  7. Nontangential maximal functions and harmonic conjugates
  8. The Smirnov Class
  9. Equivalence of Definitions of Hardy Space

Key Result

Lemma \oldthetheorem

Suppose that the modular family $\Phi$ is slowly changing on intervals. Then for any $B > 0$ there is a constant $C$ such that if $\rho(f) \leq B$ then on each interval $I$ in the level set of $\{x: f(x) > \lambda\}$ we have $\Phi_{I, +}(\lambda) \leq C \Phi_{I, -}(\lambda)$.

Theorems & Definitions (47)

  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Lemma \oldthetheorem
  • Example \oldthetheorem
  • Example \oldthetheorem
  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • proof
  • ...and 37 more