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Complementary Results on the Boundedness Problem of Factorizable Four-Dimensional Matrices

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Abstract

In this paper, the boundedness problem of factorizable four-dimensional matrices on the space of double sequences is investigated. As an application of our results, the lower bounds and the operator norms of four-dimensional Cesàro matrix and four-dimensional Copson matrix are obtained, which provide an extension of Hardy’s discrete inequality and Copson’s discrete inequality to double series, respectively. Finally, we present complementary results for the operator norm and lower bound of the four-dimensional Hausdorff matrices.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, 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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Communicated by Fuad Kittaneh.

The paper is dedicated to the doyen of the martyrs, the chief of the youth of paradise, Imam Hossein ibn Ali (peace be upon him) in the memory of the 1379th occasion of his Arbaeen.

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Talebi, G. Complementary Results on the Boundedness Problem of Factorizable Four-Dimensional Matrices. Bull. Malays. Math. Sci. Soc. 43, 609–618 (2020). https://doi.org/10.1007/s40840-018-00703-7

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  • DOI: https://doi.org/10.1007/s40840-018-00703-7

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