Norm inequalities for derivatives and differences
By: Man Kam Kwong, Anton Zettl.
Contributors: Zettl, Anton.
Series: Lecture notes in mathematics ;; 1536; Lecture notes in mathematics (Springer-Verlag) ;; 1536.
Publisher: Springer-Verlag
Published: 1992
Place of publication: Berlin; New York
Language: eng
Number of pages: 150
Subjects: Inequalities (Mathematics); Difference equations
Description: 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.
Notes: Includes bibliographical references (p. 144-148) and index.