数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1411-1425.doi: 10.1016/S0252-9602(15)30063-1

• 论文 • 上一篇    下一篇

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESÁRO TYPE

Ha Duy HUNG1, Luong Dang KY2   

  1. 1. High School for Gifted Students, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam;
    2. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • 收稿日期:2015-04-13 修回日期:2014-08-07 出版日期:2015-11-01 发布日期:2015-11-01
  • 通讯作者: Luong Dang KY, E-mail: luongdangky@tdt.edu.vn E-mail:luongdangky@tdt.edu.vn
  • 作者简介:Ha Duy HUNG, E-mail: hunghaduy@gmail.com
  • 基金资助:

    The first author is supported by Vietnam National Foundation for Science and Technology Development (101.02-2014.51).

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESÁRO TYPE

Ha Duy HUNG1, Luong Dang KY2   

  1. 1. High School for Gifted Students, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam;
    2. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Received:2015-04-13 Revised:2014-08-07 Online:2015-11-01 Published:2015-11-01
  • Contact: Luong Dang KY, E-mail: luongdangky@tdt.edu.vn E-mail:luongdangky@tdt.edu.vn
  • Supported by:

    The first author is supported by Vietnam National Foundation for Science and Technology Development (101.02-2014.51).

摘要:

This paper deals with a general class of weighted multilinear Hardy-Cesàro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesàro operators (with symbols in central BMO spaces) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.

关键词: Hardy-Cesà, ro operators, Hardy's inequality, multilinear Hardy operator, weig-hted Hardy-Littlewood averages

Abstract:

This paper deals with a general class of weighted multilinear Hardy-Cesàro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesàro operators (with symbols in central BMO spaces) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.

Key words: Hardy-Cesà, ro operators, Hardy's inequality, multilinear Hardy operator, weig-hted Hardy-Littlewood averages

中图分类号: 

  • 42B35(46E30