| 1. |
- Aldaz, J. M., et al.
(författare)
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Advances in Operator Cauchy-Schwarz Inequalities and their Reverses
- 2015
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Ingår i: Annals of Functional Analysis. - : Tusi Mathematical Research Group. - 2008-8752. ; 6:3, s. 275-295
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Tidskriftsartikel (refereegranskat)abstract
- The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert C*-modules. In particular, we pay special attention to an operator Wielandt inequality.
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| 2. |
- Flodén, Liselott, 1967-, et al.
(författare)
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Detection of scales of heterogeneity and parabolic homogenization applying very weak multiscale convergence
- 2011
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Ingår i: Annals of Functional Analysis. - Mashdad, Iran : TSMG. - 2008-8752. ; 2:1, s. 84-99
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Tidskriftsartikel (refereegranskat)abstract
- We apply a new version of multiscale convergence named very weak multiscale convergence to find possible frequencies of oscillation in an unknown coefficient of a diffeential equation from its solution. We also use thís notion to study homogenization of a certain linear parabolic problem with multiple spatial and temporal scales
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| 3. |
- Oguntuase, James, et al.
(författare)
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Time scales Hardy-type inequalities via superquadracity
- 2014
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Ingår i: Annals of Functional Analysis. - : Springer Science and Business Media LLC. - 2008-8752. ; 5:2, s. 61-73
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Tidskriftsartikel (refereegranskat)abstract
- In this paper some new Hardy-type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy-type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed
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| 4. |
- Persson, Lars-Erik, et al.
(författare)
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On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces
- 2018
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Ingår i: Annals of Functional Analysis. - : Duke University Press. - 2008-8752. ; 9:1, s. 137-150
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient.
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