Inequalities Based on Sobolev Representations [Paperback]

Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Gr?ss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. ?Applications?illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. ?The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory.

Inequalities based on Sobolev Representations deals exclusively with tight integral inequalities of Chebyshev-Gr?ss and Ostrowski types, and of integral means. Applications?illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions.

?Part 1. -Univariate Integral Inequalities based on Sobolev representations.- Introduction.- Background. -Main Results. -Applications.- References.? Part 2.- Multivariate Integral Inequalities deriving from Sobolev representations.-Introduction.-Background.-Main Results.- Applications, References.

First monograph to deal exclusively with very general tight integral inequalities of Chebyshev-Gr?ss, Ostrowski types and of comparison of integral means

Advanced courses and seminars can be taught out of this book

All necessary background and motivations are given in each chapter

Suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory