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- Gogatishvili, Amiran, et al.
(författare)
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Compactness of the Hardy operator and its limiting case
- 2006
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Ingår i: Soochow Journal of Mathematics. - 0250-3255. ; 32:1, s. 21-35
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Tidskriftsartikel (refereegranskat)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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- Gogatishvili, Amiran, et al.
(författare)
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Some new scales of characterization of Hardy's inequality
- 2010
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1736-6046 .- 1736-7530. ; 59:1, s. 7-18
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Tidskriftsartikel (refereegranskat)abstract
- Let 1 < p ≤ q < ∞. Inspired by some recent results concerning Hardy-type inequalities where the equivalence of four scales of integral conditions was proved, we use related ideas to find ten new equivalence scales of integral conditions. By applying this result to the original Hardy-type inequality, we obtain a new proof of a number of characterizations of the Hardy inequality and also some new weight characterizations.
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- Gogatishvili, Amiran, et al.
(författare)
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Some new scales of weight characterizations of the class Bp
- 2009
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Ingår i: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 123:4, s. 365-377
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Tidskriftsartikel (refereegranskat)abstract
- We present an equivalence theorem, which includes all known characterizations of the class B p , i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p *, B ∞ * and RB p , and prove and apply a "gluing lemma" of independent interest.
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- Gogatishvili, Amiran, et al.
(författare)
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Weighted Stieltjes inequality and applications
- 2013
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 286:7, s. 659-668
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Tidskriftsartikel (refereegranskat)abstract
- Let 1 < p ≤ q < ∞. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions.
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- Heinig, Hans P., et al.
(författare)
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On some fractional order Hardy inequalities
- 1997
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 1:1, s. 25-46
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Tidskriftsartikel (refereegranskat)abstract
- Weighted inequalities for fractional derivatives (= fractional order Hardy-type inequalities) have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.
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