数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 429-436.doi: 10.1007/s10473-022-0124-x

• 论文 • 上一篇    

OPERATOR NORM AND LOWER BOUND OF FOUR-DIMENSIONAL GENERALIZED HAUSDORFF MATRICES

Gholamreza TALEBI   

  1. Department of Mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran
  • 收稿日期:2020-05-19 修回日期:2020-09-22 出版日期:2022-02-25 发布日期:2022-02-24
  • 作者简介:Gholamreza TALEBI,E-mail:Gh.talebi@vru.ac.ir

OPERATOR NORM AND LOWER BOUND OF FOUR-DIMENSIONAL GENERALIZED HAUSDORFF MATRICES

Gholamreza TALEBI   

  1. Department of Mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran
  • Received:2020-05-19 Revised:2020-09-22 Online:2022-02-25 Published:2022-02-24

摘要: The problem addressed is the exact determination of the operator norm and lower bound of four-dimensional generalized Hausdorff matrices on the double sequence spaces $\mathcal{L}_p$. A Hardy type formulae is found as an exact value for their operator norm and a Copson type formulae is established as a lower estimate for their lower bound. Further, exact values are found for the operator norm and lower bound of the transpose of generalized Hausdorff matrices.

Abstract: The problem addressed is the exact determination of the operator norm and lower bound of four-dimensional generalized Hausdorff matrices on the double sequence spaces $\mathcal{L}_p$. A Hardy type formulae is found as an exact value for their operator norm and a Copson type formulae is established as a lower estimate for their lower bound. Further, exact values are found for the operator norm and lower bound of the transpose of generalized Hausdorff matrices.

中图分类号: 

  • 46A45