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Sobolev spaces on hypergroups Gelfand pairs

Ky T. Bataka, Murphy E. Egwe, Yaogan Mensah

Abstract

This paper introduces Sobolev spaces over Gelfand pairs in the framework of hypergroups. The Sobolev spaces in question are constructed from the Fourier transform on hypergroup Gelfand pairs. Mainly, the paper focuses on the investigation of Sobolev embedding results.

Sobolev spaces on hypergroups Gelfand pairs

Abstract

This paper introduces Sobolev spaces over Gelfand pairs in the framework of hypergroups. The Sobolev spaces in question are constructed from the Fourier transform on hypergroup Gelfand pairs. Mainly, the paper focuses on the investigation of Sobolev embedding results.
Paper Structure (3 sections, 8 theorems, 22 equations)

This paper contains 3 sections, 8 theorems, 22 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Sobolev spaces on the hypergroup Gelfand pairs $(G,K)$

Key Result

Theorem 2.5

Let $(G,K)$ be a hypergroup Gelfand pair. There exists a unique nonnegative measure $\pi$ on $\widehat{G^\natural}$ such that

Theorems & Definitions (21)

  • Definition 2.1: Brou
  • Definition 2.2: Brou2
  • Definition 2.3
  • Definition 2.4: Brou
  • Theorem 2.5: Brou
  • Definition 3.1
  • Theorem 3.2
  • proof
  • Corollary 3.3
  • Theorem 3.4
  • ...and 11 more