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| 5. |
- Bergh, Jöran, et al.
(författare)
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On some sharp reversed Hölder and Hardy type inequalities
- 1994
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 169:1, s. 19-29
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Tidskriftsartikel (refereegranskat)abstract
- We discuss some reversed Hölder inequalities yielding for functions on R+ satisfying one or two conditions of quasi-monotonicity. All cases of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed inequalities of Hardy type for quasi-monotone functions. In some cases we obtain the best constants and all cases of equality are obtained. Some applications, open questions and the relations to other similar results are pointed out.
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- Dechevski, Ljubomir T., et al.
(författare)
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Sharp generalized Carleman inequalities with minimal information about the spectrum
- 1994
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 168:1, s. 61-77
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Tidskriftsartikel (refereegranskat)abstract
- Let H and T: H → H denote a separable Hilbert space and an operator in a Schatten-von Neumann ideal Sp(H), respectively. Consider the resolvent operator (λI - T)−1, where I is the identity operator and λ belongs to the resolvent set of T. Some sharp bounds for the uniform operator norm of (λI - T)−1 are derived in some situations of particular interest for certain applications, namely when only partial or minimal information about the spectrum is available. The results obtained may also be regarded as generalizations of Carleman's inequality for quasinilpotent operators.
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- Holmbom, Anders, et al.
(författare)
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A homogenization procedure for computing effective moduli and microstresses in elastic composite materials
- 1992
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Ingår i: Composites Engineering. - 0961-9526. ; 2:4, s. 249-259
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Tidskriftsartikel (refereegranskat)abstract
- Effective properties and microstress variations of elastic fiber composites are studied by means of the homogenization method. Some numerical results are obtained by using the finite element code HOMO. The model problem is a two-phase elastic fiber composite consisting of boron fibers in an epoxy matrix with various fractions of the two phases. The homogenized stiffness matrices are compared with the weighted harmonic and arithmetic means, respectively.
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- Johansson, Hans, et al.
(författare)
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Inequalities for moduli of continuity and rearrangements
- 1991
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Ingår i: Conference on Approximation Theory, in Kecskemét, August 6 to 11, 1990. - : Elsevier. - 0444986952 ; , s. 412-423
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Konferensbidrag (refereegranskat)abstract
- In this paper we consider measurable functions f from a symmetric space X on [0,1]. We prove some inequalities relating the behavior of the nonincreasing rearrangement f* and the (generalized) modulus of continuity ωX (t,f). In particular, we generalize, complement and unify some previous result by Brudnyi, Garsia and Rodemich, Milman, Osvald, Storozhenko, and Wik. We note that these inequalities have direct applications, e.g. in the theory of imbedding of symmetric spaces and Besov (Lipschitz) spaces, Fourier analysis and the theory of stochastic processes. This paper is organized in the following way: In Section 1 we give some basic definitions and other preliminaries. In Section 2 we present a generalization of the Storozhenko inequality to the case of symmetric spaces thereby sharpening a previous result of Milman. We also include a generalization of the Garsia-Rodemich inequality to these spaces. In Section 3 we present and prove the Brudnyi-Osvald-Wik inequality for the case of symmetric spaces.
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