Dichotomies for Lorentz spaces

Szymon Głab, Filip Strobin, Chan Woo Yang

Research output: Contribution to journalArticle

3 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 May 6

Fingerprint

Lorentz Spaces
Lp Spaces
Dichotomy
Generalization

Keywords

  • Baire category
  • Integration
  • Lorentz spaces
  • Porosity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Dichotomies for Lorentz spaces. / Głab, Szymon; Strobin, Filip; Yang, Chan Woo.

In: Central European Journal of Mathematics, Vol. 11, No. 7, 06.05.2013, p. 1228-1242.

Research output: Contribution to journalArticle

Głab, Szymon ; Strobin, Filip ; Yang, Chan Woo. / Dichotomies for Lorentz spaces. In: Central European Journal of Mathematics. 2013 ; Vol. 11, No. 7. pp. 1228-1242.
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