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| 2. |
- Abramovich, Shoshana, et al.
(författare)
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Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity
- 2020
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Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 23:2, s. 447-458
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss the Hermite-Hadamard and Fejer inequalities vis-a-vis the convexity concept. In particular, we derive some new theorems and examples where Hermite-Hadamard and Fejer type inequalities are satisfied without the assumptions of convexity or concavity on the actual interval [a,b]
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| 3. |
- Akishev, Gabdolla, et al.
(författare)
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Inequalities for the Fourier coefficients in unbounded orthogonal systems in generalized Lorentz spaces
- 2020
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Ingår i: Nonlinear Studies. - : Cambridge Scientific Publishers Ltd. - 1359-8678. ; 27:4, s. 1137-1155
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Tidskriftsartikel (refereegranskat)abstract
- This paper is an essential complement of the research recently presented in [1], [2]. A number of classical Fourier inequalities related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of generalized Lorentz spaces.
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| 4. |
- Akishev, Gabdolla, et al.
(författare)
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Some New Fourier and Jackson-Nikol'skii Type Inequalities In Unbounded Orthonormal Systems
- 2021
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Ingår i: Constructive Mathematical Analysis. - : Tuncer ACAR. - 2651-2939. ; :3, s. 291-304
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Tidskriftsartikel (refereegranskat)abstract
- We consider the generalized Lorentz space L ;q dened via a continuous and concave function and the Fourier series of a function with respect to an unbounded orthonormal system. Some new Fourier and Jackson-Nikol'skii type inequalities in this frame are stated, proved and discussed. In particular, the derived results generalize and unify several well-known results but also some new applications are pointed out.
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| 5. |
- Akishev, G., et al.
(författare)
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Some new Fourier inequalities for unbounded orthogonal systems in Lorentz–Zygmund spaces
- 2020
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; , s. 1-12
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove some essential complements of the paper (J. Inequal. Appl.2019:171, 2019) on the same theme. We prove some new Fourier inequalities in thecase of the Lorentz–Zygmund function spaces Lq,r(log L)α involved and in the casewith an unbounded orthonormal system. More exactly, in this paper we prove anddiscuss some new Fourier inequalities of this type for the limit case L2,r(log L)α, whichcould not be proved with the techniques used in the paper (J. Inequal. Appl.2019:171, 2019).
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| 6. |
- Algervik, Robert, 1981-
(författare)
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Embedding Theorems for Mixed Norm Spaces and Applications
- 2008
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. The work in this direction originates in a paper due to Gagliardo (1958), and was continued by Fournier (1988) and by Kolyada (2005). We consider fully anisotropic mixed norm spaces. Our main theorem states an embedding of these spaces into Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic fractional Sobolev spaces and anisotropic Sobolev-Besov spaces. The methods used are based on non-increasing rearrangements and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces $B_p^\alpha$ by Bourgain, Brezis, and Mironescu, and for Besov spaces $B^{\alpha_1,\dots,\alpha_n}_p$ by Kolyada. We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces and in the description of Sobolev type embeddings.
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| 7. |
- Aljinovic, Andrea Aglic, et al.
(författare)
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Josip Pecaric- and his life in mathematics and politics
- 2019
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Ingår i: Mathematical Inequalities & Applications. - : Element. - 1331-4343 .- 1848-9966. ; 22:4, s. 1067-1080
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Tidskriftsartikel (refereegranskat)abstract
- It is impossible in limited number of pages to give a fair picture of such a remarkable man, great mathematician and human being as Josip Pecaric. Our intention is instead to complement the picture of him in various ways. We hope that our paper will give also someflavor of Josip as family man, fighter, supervisor,international authority, author (also in other subjects than mathematics), fan of the Croatian football team, and not only as his obvious role as our King of Inequalities.
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| 8. |
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| 9. |
- Andersson-Sköld, Yvonne, et al.
(författare)
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Landslide risk management : A brief overview and example from Sweden of current situation and climate change
- 2013
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Ingår i: International Journal of Disaster Risk Reduction. - : Elsevier. - 2212-4209. ; 3:March, s. 44-61
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Tidskriftsartikel (refereegranskat)abstract
- Landslide risk is a function of the probability of the event and its consequences. Previous research has shown that preventive measures to reduce the risk are preferred over reactive measures but, especially in developing countries, rarely undertaken. A contributing factor is the lack of evidence that preventive measures pay. This study includes a brief overview of landslide risk management in general and an investigation of the present risk management situation in Sweden based on interviews in 11 municipalities complemented with interviews in Norway. The result shows that climate change has become part of the general awareness and started to be taken into account in the municipal spatial planning. Landslide susceptibility maps and databases are useful tools in the complex spatial planning. The results indicate that the application of landslide susceptibility and risk maps as previously applied for preventive measures and spatial planning in the landslide prone area Gota alv river valley have been cost effective. Improved documentation and more active communication among different stakeholders would, however, contribute to more effective landslide management.
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| 10. |
- Baramidze, David, et al.
(författare)
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(H-p - L-p)-Type inequalities for subsequences of Norlund means of Walsh-Fourier series
- 2023
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2023:1
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the subsequence {t2n f} of Norlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H-p to the space weak-Lp for 0 < p < 1/(1+ alpha), where 0 < alpha < 1. Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Norlund logarithmic means and Cesaro means.
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