Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multilinear Square Operators Meet New Weight Functions

Chunliang Li, Shuhui Yang, Yan Lin

Abstract

Via the new weight $A_{\vec p}^{θ}(\varphi )$, the authors introduce a new class of multilinear square operators. The boundedness on the weighted Lebesgue space and the weighted Morrey space is obtained, respectively. Our results include the known results of the standard multilinear square operator and the weight $A_{\vec p}$. Moreover, the results in this article seem to be new even for one-linear case.

Multilinear Square Operators Meet New Weight Functions

Abstract

Via the new weight , the authors introduce a new class of multilinear square operators. The boundedness on the weighted Lebesgue space and the weighted Morrey space is obtained, respectively. Our results include the known results of the standard multilinear square operator and the weight . Moreover, the results in this article seem to be new even for one-linear case.
Paper Structure (7 sections, 12 theorems, 72 equations, 1 figure)

This paper contains 7 sections, 12 theorems, 72 equations, 1 figure.

Table of Contents

  1. Introduction
  2. New weighted norm inequalities on Lebesgue spaces
  3. Definitions and lemmas
  4. Main theorem and its proof
  5. New weighted norm inequalities on new Morrey spaces
  6. Necessary lemmas
  7. Main theorem and its proof

Key Result

Lemma 2.1

(b1) The following statements are established.

Figures (1)

  • Figure 1: Relation among of several classes of multilinear square operators and weight functions

Theorems & Definitions (22)

  • Remark 1.1
  • Remark 1.2
  • Remark 1.3
  • Remark 1.4
  • Definition 1.1
  • Remark 1.5
  • Definition 2.1
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • ...and 12 more