Norm Inequalities for Derivatives and Differences [electronic resource] / by Man Kam Kwong, Anton Zettl.

By:

Kwong, Man Kam [author.]

Contributor(s):

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1536Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992Description: VIII, 152 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540475484

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

515.8 23

LOC classification:

QA331.5

Online resources:

Click here to access online

Contents:

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

In: Springer eBooksSummary: 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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Unit weight functions -- The norms of y,y?,y? -- Weights -- The difference operator.

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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