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Operator norm and lower bound of four-dimensional generalized Hausdorff matrices

Acta Mathematica Scientia volume 42, pages 429–436 (2022)Cite this article

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 \(\cal{L}_{p}\). 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.

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Acknowledgements

We would like to thank Professor Graham Jameson and Professor Billy E. Rhoades for their technical assistance during the preparation of the present paper.

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Authors and Affiliations

  1. Department of Mathematical sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran

    Gholamreza Talebi

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  1. Gholamreza Talebi
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Correspondence to Gholamreza Talebi.

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The paper is dedicated to the national hero of Iranian: Martyr Haj Qasem Soleimani

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Talebi, G. Operator norm and lower bound of four-dimensional generalized Hausdorff matrices. Acta Math Sci 42, 429–436 (2022). https://doi.org/10.1007/s10473-022-0124-x

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  • DOI: https://doi.org/10.1007/s10473-022-0124-x

Key words

  • four-dimensional Hausdorff matrices

2010 MR Subject Classification

  • 46A45
  • 40G05