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 language | English |
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Pages (from-to) | 1228-1242 |
Number of pages | 15 |
Journal | Central European Journal of Mathematics |
Volume | 11 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Baire category
- Integration
- Lorentz spaces
- Porosity
ASJC Scopus subject areas
- Mathematics(all)