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Bounds for $p$-adic Hardy-type Operators and Commutator On $p$-adic Variable Herz-Morrey Spaces

Samia Bashir, Amjad Hussain

Abstract

This paper showed that fractional p-adic Hardy operator norms in p-adic Herz-Morrey spaces with varying exponents are bounded. Corresponding commutator operators are also estimated for p-adic variable central bounded mean oscillations (CBMO).

Bounds for $p$-adic Hardy-type Operators and Commutator On $p$-adic Variable Herz-Morrey Spaces

Abstract

This paper showed that fractional p-adic Hardy operator norms in p-adic Herz-Morrey spaces with varying exponents are bounded. Corresponding commutator operators are also estimated for p-adic variable central bounded mean oscillations (CBMO).
Paper Structure (6 sections, 12 theorems, 36 equations)

This paper contains 6 sections, 12 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Some Function Spaces
  4. Fractional p-adic Hardy operator
  5. Variable $p$-adic Herz Space Estimates for Hardy Operators
  6. Variable Morrey-Herz Estimates for $p$-adic Hardy-type Operators and Commutators

Key Result

Lemma 2.5

C2.18 Assume that $u\in\mathfrak{G}(\mathbb{Q}^{n}_{p})$ is an L-Lipschitz function for a value of $L\geq0,$ then $u\in W_{0}(\mathbb{Q}^{n}_{p}).$

Theorems & Definitions (16)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Lemma 2.7
  • Lemma 2.8
  • Theorem 3.1
  • Corollary 3.2
  • ...and 6 more