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Equivalent norms for polynomials on the sphere

Jordi Marzo, Joaquim Ortega-Cerdà

Abstract

We study comparison of Lp norms of polynomials on the sphere with respect to doubling measures. From our description it follows an uncertainty principle for square integrable functions on the sphere. We consider also weighted uniform versions of this result.

Equivalent norms for polynomials on the sphere

Abstract

We study comparison of Lp norms of polynomials on the sphere with respect to doubling measures. From our description it follows an uncertainty principle for square integrable functions on the sphere. We consider also weighted uniform versions of this result.

Paper Structure

This paper contains 4 sections, 9 theorems, 74 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries and Statements
  3. Main Results
  4. Uniform norm case

Key Result

Theorem 1

Let $\Omega$ be a bounded set and let $1\le p<+\infty$. A set $E\subset \mathbb{R}^d$ satisfies if and only if there is a cube $K\subset \mathbb{R}^{d}$ such that

Figures (1)

  • Figure 1:

Theorems & Definitions (24)

  • Theorem : Logvinenko-Sereda
  • Theorem
  • Corollary 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Theorem 1.5
  • Definition 1.6
  • Remark
  • Lemma 1.7
  • ...and 14 more