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| 3. |
- Gogatishvili, Amiran, et al.
(author)
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Compactness of the Hardy operator and its limiting case
- 2006
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In: Soochow Journal of Mathematics. - 0250-3255. ; 32:1, s. 21-35
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Journal article (peer-reviewed)abstract
- Let 1 < p q < 1: Inspired by some recent results concerning Hardy type inequalities where the equivalence of four scales of integral conditions is proved, we use related ideas to prove some new compactness results for the Hardy operator, and we give the corresponding scales for the Polya-Knopp inequality.
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| 4. |
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| 5. |
- Jain, Pankaj, et al.
(author)
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Carleman-Knopp type inequalities via Hardy inequalities
- 2001
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 4:3, s. 343-355
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Journal article (peer-reviewed)abstract
- Some new Carleman-Knopp type inequalities are proved as "end point" inequalities of modern forms of Hardy's inequalities. Both finite and infinite intervals are considered and both the cases p q and q < p are investigated. The obtained results are compared with similar results in the literature and the sharpness of the constants is discussed for the power weight case. Moreover, some reversed Carleman-Knopp inequalities are derived and applied.
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| 8. |
- Johansson, Maria, et al.
(author)
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A new approach to the Sawyer and Sinnamon characterizations of Hardy's inequality for decreasing functions
- 2008
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In: Georgian Mathematical Journal. - 1072-947X .- 1572-9176. ; 15:2, s. 295-306
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Journal article (peer-reviewed)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.
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| 9. |
- Johansson, Maria, et al.
(author)
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Carleman's inequality : history, proofs and some new generalizations
- 2003
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In: Journal of Inequalities in Pure and Applied Mathematics. - 1443-5756. ; 4:3
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Journal article (peer-reviewed)abstract
- Carleman's inequality reads where , are positive numbers. In this paper we present some simple proofs of and several remarks (e.g. historical) about the inequality and its corresponding continuous version. Moreover, we discuss and comment on some very new results. We also include some new proofs and results e.g. a weight characterization of a general weighted Carleman type inequality for the case 0 p q We also include some facts about T. Carleman and his work.
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