Dichotomies for Lorentz spaces

Szymon Głab, Filip Strobin, Chan Woo Yang

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number7
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.


  • Baire category
  • Integration
  • Lorentz spaces
  • Porosity

ASJC Scopus subject areas

  • General Mathematics


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