The best constant in a fractional Hardy inequality
✍ Scribed by Krzysztof Bogdan; Bartłomiej Dyda
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 125 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We prove an optimal Hardy inequality for the fractional Laplacian on the half‐space. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
📜 SIMILAR VOLUMES
In this paper, the best approximating form of constant e and Hardy's inequality are discussed, and the improved conclusions of earlier work are achieved. w x Recently, Y. Bicheng 1, 2 attained the inequalities involving constant e, x 1 1 1 e 1 y -1 q e 1 y , 1 Ž . ž / ž / 2 x q 1 x 2 x q 1 Ž .
## An additive form of the Landau inequality for is proved for 0<c (cos(?Â2n)) &2 , 1 m n&1, with equality for , where T n is the Chebyshev polynomial. From this follows a sharp multiplicative inequality, For these values of \_, the result confirms Karlin's conjecture on the Landau inequality f
In this note, it is shown that the Hardy᎐Hilbert inequality for double series can Ž . be improved by introducing a proper weight function of the form rsin rp y Ž . 1y1rr Ž Ž . . O n rn with O n ) 0 into either of the two single summations. When r r r s 2, the classical Hilbert inequality is improved
## Abstract We consider the Laplacian in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to a Hardy inequality for the Laplacian. As a byproduct of our method, we obtain a simple proof of a th