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Marcinkiewicz integrals associated with Schrödinger operator on Campanato type spaces

Qingying Xue, Jiali Yu

Abstract

The boundedness of the Marcinkiewicz integrals associated with Schrödinger operator from the localized Morrey-Campanato space to the localized Morrey-Campanato-BLO space is established. Similar results for the Marcinkiewicz integrals associated with the Schrödinger operator with rough kernels were also investigated.

Marcinkiewicz integrals associated with Schrödinger operator on Campanato type spaces

Abstract

The boundedness of the Marcinkiewicz integrals associated with Schrödinger operator from the localized Morrey-Campanato space to the localized Morrey-Campanato-BLO space is established. Similar results for the Marcinkiewicz integrals associated with the Schrödinger operator with rough kernels were also investigated.
Paper Structure (4 sections, 14 theorems, 156 equations)

This paper contains 4 sections, 14 theorems, 156 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem \ref{['th1']}
  4. Proof of Theorem \ref{['th3']}

Key Result

Theorem 1.1

Let $V\in\mathcal{B}_n\ p\in (1,+\infty),\ 0<\delta<2-\frac{n}{q_0},\ 0<\gamma<1-\frac{n}{q_0},\ 0<\beta<\min \{1,1-\frac{n}{q_0}\}.$ If $\alpha\in\left(-\infty,\frac{1}{n}\min\{{\delta},{1-2\delta},\frac{\gamma}{2},\frac{\beta}{2},\frac{1}{3}\}\right)$, then for each $j,$$1\le j\le n$, $\mu{_j^\mat

Theorems & Definitions (24)

  • Definition 1.1: CHMY1
  • Definition 1.2
  • Remark 1.3
  • Theorem 1.1
  • Theorem 1.2
  • Corollary 1.3
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • ...and 14 more