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- Gogatishvili, Amiran, et al.
(författare)
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Characterisation of embeddings in Lorentz spaces
- 2007
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Ingår i: Bulletin of the Australian Mathematical Society. - 0004-9727 .- 1755-1633. ; 76:1, s. 69-92
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Tidskriftsartikel (refereegranskat)abstract
- Some new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embeddingSome new integral conditions characterising the embedding Λp(v) → Γq(w), 0 < p, q ≤ co are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) 1 = ∞, 1 < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space Γuq(w). In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding
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| 2. |
- Oguntuase, James, et al.
(författare)
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Mulitdimensional Hardy type inequalities for p
- 2007
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Ingår i: Journal of Mathematical Inequalities. - : Element d.o.o.. - 1846-579X .- 1848-9575. ; 1:1, s. 1-11
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Tidskriftsartikel (refereegranskat)
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| 3. |
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| 4. |
- Oguntuase, James, et al.
(författare)
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Weighted multidimensional Hardy type inequalities via Jensen's inequality
- 2007
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Ingår i: Proceedings of A. Razmadze Mathematical Institute. - 1512-0007. ; 144, s. 91-105
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Tidskriftsartikel (refereegranskat)abstract
- The authors prove that Jenson's inequality implies some sharp weighted multidimensional Hardy type inequalities. In particular, their results unify and further extend several results of this type in the literature including the recent results in [A. Čižmešija, J. E. Pečarić and L. E. Persson, J. Approx. Theory 125 (2003), no. 1, 74--84; MR2016841 (2004i:42017); S. Kaijser et al., Math. Inequal. Appl. 8 (2005), no. 3, 403--417; MR2148234 (2006c:26036); S. Kaijser, L. E. Persson and A. Öberg, J. Approx. Theory 117 (2002), no. 1, 140--151; MR1920123 (2003f:26037)]. The main result is obtained in Theorem 3.1. In Section 4, the authors show that some existing results are special cases of the theorems obtained in this paper.
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| 5. |
- Okpoti, Christopher, et al.
(författare)
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An equivalence theorem for some integral conditions with general measures related to Hardy´s inequality
- 2007
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 326:1, s. 398-413
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Tidskriftsartikel (refereegranskat)abstract
- It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<pq<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.
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| 8. |
- Okpoti, Christopher, et al.
(författare)
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An equivalence theorem for some integral conditions with general measures related to Hardy's inequality II
- 2008
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 337:1, s. 219-230
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Tidskriftsartikel (refereegranskat)abstract
- Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 01. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures.
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