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Norm Inequalities for Derivatives and Differences
Autor: Kwong, Man Kam
Rok: 1992
ISBN: 9783540563877
ISBN: 9780387563879
OKCZID: 110103790
Citace (dle ČSN ISO 690):
KWONG, Man Kam a Anton ZETTL. Norm inequalities for derivatives and differences. Berlin: Springer-Verlag, c1992, 150 s. Lecture notes in mathematics, 1536. ISBN 3-540-56387-3.
Anotace
Norm inequalities relating (i) a function and two of its derivatives and (ii) a sequence and two of its differences are studied. Detailed elementary proofs of basic inequalities are given. These are accessible to anyone with a background of advanced calculus and a rudimentary knowledge of the Lp and lp spaces. The classical inequalities associated with the names of Landau, Hadamard, Hardy and Littlewood, Kolmogorov, Schoenberg and Caravetta, etc., are discussed, as well as their discrete analogues and weighted versions. Best constants and the existence and nature of extremals are studied and many open questions raised. An extensive list of references is provided, including some of the vast Soviet literature on this subject.