ENGLISH

Norm Inequalities for Derivatives and Differences

By Anton Zettl (auth.) , Man Kam Kwong

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1992
ISBN
3540563873, 9783540563877
DOI
10.1007/BFb0090864
LCC
QA3 .L28 no. 1536,QA295 .L28 no. 1536
Open Library ID
OL1737007M
Language
english
Format
DJVU
Filesize
848 kB (868031 bytes)
Series
Lecture Notes in Mathematics 1536
Edition
1
Pages
152\156
Library
Kolxo3
DPI
300
Time added
2011-07-22 07:35:22
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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