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Maximal $Λ(p)$-subsets of manifolds

Ciprian Demeter, Hongki Jung, Donggeun Ryou

Abstract

We construct maximal $Λ(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.

Maximal $Λ(p)$-subsets of manifolds

Abstract

We construct maximal -subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents . Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.

Paper Structure

This paper contains 5 sections, 30 theorems, 137 equations.

Table of Contents

  1. Description of tight decoupling in Rd
  2. A general answer for Question Q1
  3. decoupling estimates; deterministic examples
  4. $l^p$ analogs
  5. Probabilistic estimates

Key Result

Theorem 1.1

For each orthonormal system $\Phi=\{\varphi_1,\ldots,\varphi_N\}$ of functions with $\|\varphi_n\|_{L^\infty}\le 1$ and each $p>2$, there is $\Psi\subset \Phi$ with size $\sim N^{2/p}$ such that The implicit constant is independent of $N$.

Theorems & Definitions (52)

  • Theorem 1.1: Bo
  • Proposition 1.3
  • Theorem 2.1
  • Corollary 2.2
  • proof
  • Theorem 2.3
  • proof
  • Proposition 2.4
  • Lemma 2.5
  • Proposition 2.6
  • ...and 42 more