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On the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent

Boukary Tai, Mohamed Congo, Marie Françoise Ouedraogo, Arouna Ouedraogo

Abstract

The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(ρ, δ)$ which symbols belong to the Hörmander class $S^{m}_{ρ, δ}(\mathbb{T}^{n}\times\mathbb{Z}^{n})$ for $0\leqδ<ρ\leq1.$

On the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent

Abstract

The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent on the -dimensional torus. We deal with operators of type which symbols belong to the Hörmander class for

Paper Structure

This paper contains 6 sections, 12 theorems, 67 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. On the torus
  4. On periodic Fourier integral operators
  5. Some basic tools on variable exponent and weight functions
  6. Mains results

Key Result

Lemma 2.3

Assume that $\varphi, \psi:\mathbb{Z}^{n}\rightarrow \mathds{C}$. Then for all $\alpha\in\mathbb{N}^{n}$, provided that both series are absolutely convergent.

Theorems & Definitions (26)

  • Definition 2.1
  • Definition 2.2
  • Lemma 2.3: RT Lemma 3.3.10
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Lemma 2.7
  • Theorem 2.8
  • Definition 2.9
  • Theorem 2.10: P Theorem 2.1
  • ...and 16 more