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A note on Carleson sets and Carleson windows

Mohammad Ansari

Abstract

Let $\Bbb D$ be the open unit disk in the complex plane. In this note, for the Carleson set $S(b,h)$ and the Carleson window $W(b,h)$ which are particular subsets of $\Bbb D$, we find conditions on $h$ under which we have $W(b,h/c)\subset S(b,h)\subset W(b,ch)$ for some $c>1$.

A note on Carleson sets and Carleson windows

Abstract

Let be the open unit disk in the complex plane. In this note, for the Carleson set and the Carleson window which are particular subsets of , we find conditions on under which we have for some .
Paper Structure (2 sections, 2 theorems, 12 equations)

This paper contains 2 sections, 2 theorems, 12 equations.

Table of Contents

  1. Introduction
  2. The inclusions between Carleson sets and windows

Key Result

Proposition 1.1

Assume that $b\in \Bbb T$ and $0<h<1$. Then the inclusion $S(b,h)\subset W(b,h)$ cannot hold.

Theorems & Definitions (6)

  • Proposition 1.1
  • proof
  • Theorem 2.1
  • proof
  • Remark 2.2
  • Example 2.3