ENGLISH

Norm Inequalities for Derivatives and Differences

By Anton Zettl (auth.) , Man Kam Kwong

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1992
ISBN
978-3-540-56387-7, 978-3-540-47548-4
DOI
10.1007/BFb0090864
Language
english
Format
PDF
Filesize
2 MB (1884633 bytes)
Series
Lecture Notes in Mathematics 1536
Edition
1
Pages
152\156
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Real Functions

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.

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