Dichotomies for Lorentz spaces

Szymon Głab, Filip Strobin, Chan Woo Yang

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Assume that Lp,q, Lp1, q1,..., LLpn, qn are Lorentz spaces. This article studies the question: what is the size of the set We prove the following dichotomy: either E =Lp1, q1× ... × Lpn, qn or E is σ-porous in Lp1, q1× ... × Lpn, qn, provided 1/p ≠ 1/p1 + ... + 1/pn. In general case we obtain that either E = Lp1, q1× ... × Lpn, qn or E is meager. This is a generalization of the results for classical Lp spaces.

    Original languageEnglish
    Pages (from-to)1228-1242
    Number of pages15
    JournalCentral European Journal of Mathematics
    Volume11
    Issue number7
    DOIs
    Publication statusPublished - 2013

    Bibliographical note

    Funding Information:
    We are grateful to anonymous referees for a very careful reading of the text. The first author has been supported by the Polish Ministry of Science and Higher Education Grant No. N N201 414939.

    Keywords

    • Baire category
    • Integration
    • Lorentz spaces
    • Porosity

    ASJC Scopus subject areas

    • General Mathematics

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