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Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator
2005 (English)In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 4, p. 387-394Article in journal (Refereed) Published
Abstract [en]

We consider Tf= 0 x1 0 x2 f ( t1, t2) d t1 d t2 and a corresponding geometric mean operator Gf=exp ( 1/ x1 x2) 0 x1 0 x2 logf ( t1, t2) d t1 d t2 . E. T. Sawyer showed that theHardy-type inequality Tf Luq C f Lvp could be characterized by three independentconditions on the weights. We give a simple proof of the fact thatif the weight v is of product type, then in fact only onecondition is needed. Moreover, by using this information and byperforming a limiting procedure we can derive a weightcharacterization of the corresponding two-dimensional Pólya-Knopp inequality with the geometric mean operator G involved.

Place, publisher, year, edition, pages
2005. no 4, p. 387-394
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7906DOI: 10.1155/JIA.2005.387ISI: 000238986100004Scopus ID: 2-s2.0-33750069446Local ID: 654e6cb0-a629-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-7906DiVA, id: diva2:980796
Note
Validerad; 2005; 20070116 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Wedestig, Anna

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