E-raamat: Half-discrete Hilbert-type Inequalities

Yang and Debnath offer an extensive account of the theory and applications of any half-discrete Hilbert-type inequalities in a self-contained and rigorous manner using the methods of real and functional analysis, operator theory, the way of weight functions, and special functions. Throughout they emphasize proofs of the best constant factors of all inequalities. They cover recent developments in the field, improvements of the Euler-Maclaurin summation formula and applications, a half-discrete Hilbert-type inequality with a general homogeneous kernal, a half-discrete Hilbert-type inequality with a non-homogeneous kernel, multi-dimensional half-discrete Hilbert-type inequalities, and multiple half-discrete Hilbert-type inequalities. The material can help prepare graduate students and researchers to conduct their own research into Hilbert-type inequalities. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

In 1934, G. H. Hardy et al. published a book entitled “Inequalities”, in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree -one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books.This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non- homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.