Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

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    7 Citations (Scopus)


    In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in R<sup>n</sup> in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

    Original languageEnglish
    Article number281
    JournalJournal of Inequalities and Applications
    Issue number1
    Publication statusPublished - 2015 Dec 25



    • best constant
    • logarithmic Hardy inequality
    • scaling invariant space
    • Sobolev-Lorentz-Zygmund space

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Discrete Mathematics and Combinatorics

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