Lecture Notes in Mathematics

Kwong, Man K.; Zettl, Anton

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.

Details

Published by: Springer

Publication Date: 1993-01-29

Format: Paperback

ISBN-13: 9783540563877

DOI: 10.1007/BFb0090864

Dimensions: 235cm x155cm

Pages: 152