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In 1908, H. Wely published the well known Hilberts inequality. In 1925, G. H. Hardy gave an extension of it by introducing one pair of conjugate exponents. The Hilberttype inequalities are a more wide class of analysis inequalities which are including HardyHilberts inequality as the particular case. By making a great effort of mathematicians at about one hundred years, the theory of Hilberttype integral and discrete inequalities has now come into being. This book is a monograph about the theory of multiple halfdiscrete Hilberttype 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 halfdiscrete Hilberttype 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 halfdiscrete Hilberttype 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.
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