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A new class of function spaces generalizing the Arias-de-Reyna space

Jan Moldavčuk

Abstract

This paper studies the structure and properties of a rearrangement-invariant quasi-Banach space $QA_{\varphi,ψ}$ which generalizes the classical space $QA$ introduced by Arias-de-Reyna in connection with the study of the pointwise almost everywhere convergence of Fourier series. We present basic properties of $QA_{\varphi,ψ}$ and explore the relationship between $QA_{\varphi,ψ}$ and other rearrangement-invariant Banach spaces.

A new class of function spaces generalizing the Arias-de-Reyna space

Abstract

This paper studies the structure and properties of a rearrangement-invariant quasi-Banach space which generalizes the classical space introduced by Arias-de-Reyna in connection with the study of the pointwise almost everywhere convergence of Fourier series. We present basic properties of and explore the relationship between and other rearrangement-invariant Banach spaces.
Paper Structure (5 sections, 11 theorems, 132 equations)

This paper contains 5 sections, 11 theorems, 132 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic Properties
  4. Embeddings between the Lorentz spaces and QA_varphi,psi
  5. Comparison to rearrangement-invariant Banach spaces

Key Result

Theorem 1

Theorems & Definitions (26)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2
  • Lemma 3
  • proof
  • Proposition 4
  • proof
  • proof : Proof of Theorem \ref{['vlastnosti']}, first part
  • Theorem 5
  • ...and 16 more