Details

Subject(s)

• Functions of real variables [Browse]
• Difference equations—Numerical solutions [Browse]

Author

• Zettl, Anton [Browse]

Series

• Lecture Notes in Mathematics, 1536 [More in this series]
• Lecture Notes in Mathematics, 0075-8434 ; 1536 [More in this series]

Summary note

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.

Source of description

Description based on print version record.

Contents

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

Show 1 more Contents items

ISBN

3-540-47548-6

OCLC

1066184996

Doi

• 10.1007/BFb0090864

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