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.