Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces

Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    Research output: Contribution to journal › Article

    7 Citations (Scopus)

    Abstract

    In this paper, we establish the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces. More precisely, we generalize the Hardy type inequality obtained in Edmunds and Triebel (Math. Nachr. 207:79-92, 1999). The generalized inequality allows us to take the exponents appearing in the inequality more flexibly, and its optimality is discussed in detail. O'Neil's inequality and its reverse play an essential role for the proof.

    Original languageEnglish
    Article number381
    JournalJournal of Inequalities and Applications
    Volume2013
    DOIs
    Publication statusPublished - 2013 Dec

    Fingerprint

    Hardy Inequality
    Lorentz Spaces
    Sobolev Spaces
    Logarithmic
    Hardy-type Inequality
    Reverse
    Optimality
    Exponent
    Generalise
    Generalization

    Keywords

    • Critical Sobolev-Lorentz space
    • Logarithmic Hardy inequality
    • O'Neil's inequality

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Discrete Mathematics and Combinatorics

    Cite this

    Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces. / Machihara, Shuji; Ozawa, Tohru; Wadade, Hidemitsu.

    In: Journal of Inequalities and Applications, Vol. 2013, 381, 12.2013.

    Research output: Contribution to journal › Article

    Machihara, S, Ozawa, T & Wadade, H 2013, 'Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces', Journal of Inequalities and Applications, vol. 2013, 381. https://doi.org/10.1186/1029-242X-2013-381
    Machihara S, Ozawa T, Wadade H. Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces. Journal of Inequalities and Applications. 2013 Dec;2013. 381. https://doi.org/10.1186/1029-242X-2013-381
    Machihara, Shuji ; Ozawa, Tohru ; Wadade, Hidemitsu. / Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces. In: Journal of Inequalities and Applications. 2013 ; Vol. 2013.
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