Kwong, Man Kam.
Norm Inequalities for Derivatives and Differences [electronic resource] / by Man Kam Kwong, Anton Zettl. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. - VIII, 152 p. online resource. - Lecture Notes in Mathematics, 1536 0075-8434 ; . - Lecture Notes in Mathematics, 1536 .
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.
9783540475484
10.1007/BFb0090864 doi
Mathematics.
Mathematics.
Real Functions.
QA331.5
515.8
Norm Inequalities for Derivatives and Differences [electronic resource] / by Man Kam Kwong, Anton Zettl. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. - VIII, 152 p. online resource. - Lecture Notes in Mathematics, 1536 0075-8434 ; . - Lecture Notes in Mathematics, 1536 .
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.
9783540475484
10.1007/BFb0090864 doi
Mathematics.
Mathematics.
Real Functions.
QA331.5
515.8