Norm Inequalities for Derivatives and Differences

1992
ISBN: 978-3-540-56387-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1536, 152 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 254 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Zettl, Anton

Kwong, Man K.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Unit weight functions.- The norms of y,y?,y?.- Weights.- The difference operator.