Two Kinds of Multiple Half-Discrete Hilbert-Type Inequalities

In 1908, H. Wely published the well known Hilbert s inequality. In 1925, G. H. Hardy gave an extension of it by introducing one pair of conjugate exponents. The Hilbert-type inequalities are a more wide class of analysis inequalities which are including Hardy-Hilbert s inequality as the particular case. By making a great effort of mathematicians at about one hundred years, the theory of Hilbert-type integral and discrete inequalities has now come into being. This book is a monograph about the theory of multiple half-discrete Hilbert-type inequalities. Using the methods of Real Analysis, Functional Analysis and Operator Theory, the author introduces a few independent parameters to establish two kinds of multiple half-discrete Hilbert-type inequalities with the best possible constant factors. The equivalent forms and the reverses are also considered. As applications, the author also considers some double cases of multiple half-discrete Hilbert-type inequalities and a large number of examples. For reading and understanding this book, readers should hold the basic knowledge of Real analysis and Functional analysis.