| 1. |
- Abramovich, Shoshana, et al.
(författare)
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On some new developments of Hardy-type inequalities
- 2012
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Ingår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. - Melville, NY : American Institute of Physics (AIP). - 9780735411050 ; , s. 739-746
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Konferensbidrag (refereegranskat)abstract
- In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.
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| 2. |
- Abramovich, Shoshana, et al.
(författare)
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On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities
- 2015
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 18:2, s. 615-627
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.
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| 3. |
- Abramovich, Shoshana, et al.
(författare)
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Some new scales of refined Jensen and Hardy type inequalities
- 2014
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 17:3, s. 1105-1114
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Tidskriftsartikel (refereegranskat)abstract
- Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.
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| 4. |
- Barza, Sorina, 1967-, et al.
(författare)
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Some new sharp limit Hardy-type inequalities via convexity
- 2014
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2014
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Tidskriftsartikel (refereegranskat)abstract
- Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett's inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.
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| 5. |
- Burtseva, Evgeniya, 1988-, et al.
(författare)
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Multi–dimensional Hardy type inequalities in Hölder spaces
- 2018
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Ingår i: Journal of Mathematical Inequalities. - Zagreb : Element D.O.O.. - 1846-579X .- 1848-9575. ; 12:3, s. 719-729
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Tidskriftsartikel (refereegranskat)abstract
- Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.
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| 6. |
- Burtseva, Evgeniya, 1988-, et al.
(författare)
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Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces
- 2018
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Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 291:11-12, s. 1655-1665
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Tidskriftsartikel (refereegranskat)abstract
- We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).
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| 7. |
- Burtseva, Evgeniya, 1988-
(författare)
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Operators and Inequalities in various Function Spaces and their Applications
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This Licentiate thesis is devoted to the study of mapping properties of different operators (Hardy type, singular and potential) between various function spaces.The main body of the thesis consists of five papers and an introduction, which puts these papers into a more general frame.In paper A we prove the boundedness of the Riesz Fractional Integration Operator from a Generalized Morrey Space to a certain Orlicz-Morrey Space, which covers the Adams resultfor Morrey Spaces. We also give a generalization to the case of Weighted Riesz Fractional Integration Operators for a class of weights.In paper B we study the boundedness of the Cauchy Singular Integral Operator on curves in complex plane in Generalized Morrey Spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of Singular Integral Operators in Weighted Generalized Morrey Spaces.In paper C we prove the boundedness of the Potential Operator in Weighted Generalized Morrey Spaces in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation with a free term in such a space. We also give a short overview of some typical situations when Potential type Operators arise when solving PDEs.In paper D some new inequalities of Hardy type are proved. More exactly, the boundedness of multidimensional Weighted Hardy Operators in Hölder Spaces are proved in cases with and without compactification.In paper E the mapping properties are studied for Hardy type and Generalized Potential type Operators in Weighted Morrey type Spaces.
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| 8. |
- Burtseva, Evgeniya, 1988-, et al.
(författare)
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Potential type operators in PDEs and their applications
- 2017
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Ingår i: AIP Conference Proceedings. - : AIP Publishing. - 0094-243X .- 1551-7616. ; 1798
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Tidskriftsartikel (refereegranskat)abstract
- We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.
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| 9. |
- Kufner, Alois, et al.
(författare)
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Hardy type inequalities with kernels : The current status and some new results
- 2017
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Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 290:1, s. 57-65
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Tidskriftsartikel (refereegranskat)abstract
- We consider the general Hardy type operator inline image where inline image is a positive and measurable kernel. To characterize the weights u and v so that inline image is still an open problem for any parameters p and q. However, for special cases the solution is known for some parameters p and q. In this paper the current status of this problem is described and discussed mainly for the case inline image In particular, some new scales of characterizations in classical situations are described, some new proofs and results are given and open questions are raised.
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| 10. |
- Kufner, Alois, et al.
(författare)
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Some New Scales of Weight Characterizations of Hardy-type Inequalities
- 2013
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Ingår i: Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. - Basel : Encyclopedia of Global Archaeology/Springer Verlag. - 9783034805360 - 9783034805377 ; , s. 261-274
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Bokkapitel (refereegranskat)abstract
- In this paper we present, discuss and illustrate some new scales of conditions to characterize modern forms of Hardy′s inequalities which can not be found in the newest books in this area. Moreover, some results of importance as motivation for these scales are presented and discussed in a historical perspective.
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