Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p
2007 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, Vol. 10, no 2, 267-279 p.Article in journal (Refereed) Published
We consider the weighted Hardy inequality 1/q 1/p q ∞ ∞ x f p (x)v(x)dx f (t)dt u(x)dx C 0 0 0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x) 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.
Place, publisher, year, edition, pages
2007. Vol. 10, no 2, 267-279 p.
integral inequalities, weighted Hardy’s inequality
IdentifiersURN: urn:nbn:se:uu:diva-13429OAI: oai:DiVA.org:uu-13429DiVA: diva2:41199