Exact constants in generalized inequalities for intermediate derivatives
type: Item
instance of: scholarly article
title: Exact constants in generalized inequalities for intermediate derivatives
zbMATH Open document ID: 1180.41009
DOI: 10.1134/S0001434609050101
author: A. A. Lunev
author: L. L. Oridoroga
published in: Mathematical Notes
publication date: 2009-11-10T00:00:00Z
review text: Considering the Sobolev space \(W_2^n (\mathbb{R}_+)\) on the semiaxis with norm of general form defined by a quadratic polynomial in derivatives with nonnegative coefficients, the authors study the problem of exact constants \(A_{n,k}\) in inequalities of Kolmogorov-type [cf. \textit{G. A. Kalyabin}, Funct. Anal. Appl. 38, No. 3, 184--191 (2004); translation from Funkts. Anal. Prilozh. 38, No. 3, 29--38 (2004; Zbl 1079.41009); Funct. Anal. Appl. 38, No. 3, 184--191 (2004); translation from Funkts. Anal. Prilozh. 38, No. 3, 29--38 (2004; Zbl 1079.41009)]. The authors propose here a new method for finding the constants \(A_{n,k}\) in the case certain norms considered in the paper. A symmetric property for \(A_{n,k}\) is proved for the general case. The asymptotic behaviour of \(A_{n,k}\) is also studied.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 5628201
zbMATH Keywords: Sobolev space
zbMATH Keywords: Kolmogorov-type inequalities
zbMATH Keywords: intermediate derivatives
MaRDI profile type: Publication
cites work: The best extension operators for Sobolev spaces on the half-line
cites work: Best constants in Kolmogorov inequalities for the Sobolev space \(W^{n}_{2}(\mathbb R_+)\)
cites work: Sharp constants in inequalities for intermediate derivatives (the Gabushin case)
description: scientific article; zbMATH DE number 5628201