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Operator norm and lower bound of four-dimensional 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 \(\cal{L}_{p}\). 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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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