Multivariate Landau–Kolmogorov-type inequality-Reference-Cited by-同舟云学术

Multivariate Landau–Kolmogorov-type inequality

Published:1989-03 Issue:2 Volume:105 Page:335-350
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Ditzian Z.

Abstract

AbstractAssuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n that

where ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. On the equivalence of the K-functional and moduli of continuity and some applications

2. On inequalities between the upper bounds of successive derivatives of an arbitrary function on an infinite interval;Kolmogorov;Amer. Math. Soc. Transl. Series,1962

3. A many-variable Landau-Kolmogorov inequality

4. Some remarks on inequalities of Landau and Kolmogorov

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