| 1. |
- Nikolova, L., et al.
(författare)
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Refinements of continuous forms of classical inequalities
- 2021
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Ingår i: Eurasian Mathematical Journal. - : Steklov Mathematical Institute RAS. - 2077-9879. ; 12:2, s. 59-73
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Tidskriftsartikel (refereegranskat)abstract
- In this article we give refinements of the continuous forms of some classical inequalities i.e. of the inequalities which involve infinitely many functions instead of finitely many. We present new general results for such inequalities of Hölder-type and of Minkowski-type as well as for their reverses known as Popoviciu- and Bellman-type inequalities. Properties for related functionals are also established. As particular cases of these results we derive both well-known and new refinements of the corresponding classical inequalities for integrals and sums.
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| 2. |
- Arendarenko, Larissa, et al.
(författare)
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On the boundedness of some classes of integral operators in weighted Lebesgue spaces
- 2012
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Ingår i: Eurasian Mathematical Journal. - 2077-9879. ; 3:1, s. 5-17
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Tidskriftsartikel (refereegranskat)abstract
- Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case 1 < q < p < ∞ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition.
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| 3. |
- Chechkin, Gregory, et al.
(författare)
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A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant
- 2011
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Ingår i: Eurasian Mathematical Journal. - 2077-9879. ; 2:1, s. 81-103
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Tidskriftsartikel (refereegranskat)abstract
- We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space $H^1$ having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.
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| 4. |
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| 5. |
- Kopezhanova, Aigerim N.
(författare)
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Some new inequalities for the fourier transform for functions in generalized Lorentz spaces
- 2017
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Ingår i: Eurasian Mathematical Journal. - : Eurasian Mathematical Journal. - 2077-9879. ; 8:1, s. 58-66
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Tidskriftsartikel (refereegranskat)abstract
- The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities, relating functions on ℝ and their Fourier transforms, are extended and complemented in various ways. In particular, a variant of the Hardy-Littlewood-Stein inequality covering the case p ≥2 is proved and two-sided estimates are derived.
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| 6. |
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| 7. |
- Ospanov, K.N., et al.
(författare)
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Some inequalities for second order differential operators with unbounded drift
- 2015
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Ingår i: Eurasian Mathematical Journal. - : L.N. Gumilyov Eurasian National University. - 2077-9879. ; 6:2, s. 63-74
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Tidskriftsartikel (refereegranskat)abstract
- We study coercive estimates for some second-order degenerate and damped differential operators with unbounded coefficients. We also establish the conditions for invertibility of these operators.
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