Dichotomies for Lorentz spaces

Szymon Głab; Filip Strobin; Chan Woo Yang

doi:10.2478/s11533-013-0241-9

Dichotomies for Lorentz spaces

Szymon Głab^*, Filip Strobin, Chan Woo Yang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	1228-1242
Number of pages	15
Journal	Central European Journal of Mathematics
Volume	11
Issue number	7
DOIs	https://doi.org/10.2478/s11533-013-0241-9
Publication status	Published - 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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10.2478/s11533-013-0241-9

Cite this

@article{69fac44c6a3d41cfa994f8aeb22210ca,

title = "Dichotomies for Lorentz spaces",

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.",

keywords = "Baire category, Integration, Lorentz spaces, Porosity",

author = "Szymon G{\l}ab and Filip Strobin and Yang, \{Chan Woo\}",

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.",

year = "2013",

doi = "10.2478/s11533-013-0241-9",

language = "English",

volume = "11",

pages = "1228--1242",

journal = "Central European Journal of Mathematics",

issn = "1895-1074",

publisher = "Versita",

number = "7",

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TY - JOUR

T1 - Dichotomies for Lorentz spaces

AU - Głab, Szymon

AU - Strobin, Filip

AU - Yang, Chan Woo

N1 - 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.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Baire category

KW - Integration

KW - Lorentz spaces

KW - Porosity

UR - https://www.scopus.com/pages/publications/84876905422

U2 - 10.2478/s11533-013-0241-9

DO - 10.2478/s11533-013-0241-9

M3 - Article

AN - SCOPUS:84876905422

SN - 1895-1074

VL - 11

SP - 1228

EP - 1242

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 7

ER -

Dichotomies for Lorentz spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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