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Weight characterizations for the discrete Hardy inequality with kernel
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2006 (English)In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242XArticle in journal (Refereed) Published
Abstract [en]

A discrete Hardy-type inequality (∑n=1∞(∑k=1ndn,kak)qun)1/q≤C(∑n=1∞anpvn)1/p is considered for a positive "kernel" d={dn,k}, n,k∈ℤ+, and p≤q. For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant C. A sufficient condition for the inequality to hold in the general case is proved and this condition is necessary in special cases. Moreover, some corresponding results for the case when {an}n=1∞ are replaced by the nonincreasing sequences {an*}n=1∞ are proved and discussed in the light of some other recent results of this type.

Place, publisher, year, edition, pages
2006.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-14163DOI: 10.1155/JIA/2006/18030Local ID: d82a2800-e80a-11db-b9a9-000ea68e967bOAI: oai:DiVA.org:ltu-14163DiVA: diva2:987117
Note
Validerad; 2006; Bibliografisk uppgift: Paper id:: 18030; 20070111 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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