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/lp/de-gruyter/a-new-approach-to-the-sawyer-and-sinnamon-characterizations-of-hardy-s-hBG8nrlLYz
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- Publisher
- de Gruyter
- Copyright
- © Heldermann Verlag
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.2008.295
- Publisher site
- See Article on Publisher Site
Abstract
Some Hardy type inequalities for decreasing functions are characterized by one condition (Sinnamon), while others are described by two independent conditions (Sawyer). In this paper we make a new approach to deriving such results and prove a theorem, which covers both the Sinnamon result and the Sawyer result for the case where one weight is increasing. In all cases we point out that the characterizing condition is not unique and can even be chosen among some (infinite) scales of conditions.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Jun 1, 2008
Keywords: Inequalities; Hardy type inequalities; weights; decreasing function; scales of weight characterizations; Lorentz spaces; embeddings