Marcinkiewicz-Zygmund and interpolating families on the ball

This paper examines points and weights on the unit ball B d that satisfy L p , 0 < p ≤ ∞ , Marcinkiewicz-Zygmund inequalities and interpolating inequalities with respect to a doubling weight. We show some permutational results of these families and provide necessary density conditions for spaces...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 18 - 30
Main Author Li, Jiansong
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 21.02.2025
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Approximation
Ball
Beuring-Landau density
Density
Doubling weight
Fekete points
Inequalities
Interpolation
Marcinkiewicz-Zygmund inequalities
Mathematics
Mathematics and Statistics
Polynomials
Doubling weight
Ball
Interpolation
Beuring-Landau density
Marcinkiewicz-Zygmund inequalities
41A63
42A05
Fekete points
41A17
26D05
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Summary:This paper examines points and weights on the unit ball B d that satisfy L p , 0 < p ≤ ∞ , Marcinkiewicz-Zygmund inequalities and interpolating inequalities with respect to a doubling weight. We show some permutational results of these families and provide necessary density conditions for spaces of polynomials in terms of the Beuring-Landau density. These conditions are also sharp, which can be attained by the Fekete arrays on B d .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-025-03262-1