Description

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 including Hardy-Hilbert s inequality as the particular case. By making a great effort of the author et al in the world, the theory of Hilbert-type inequalities has now come into being. This book is a monograph about the topics on half-discrete Hilbert-type inequalities. Using the methods of Real Analysis, the author introduces a few independent parameters to obtain the weight functions. Some multiple half-discrete Hilbert-type inequalities with the best possible constant factors are established. The equivalent forms and the reverses are also provided. The author also considers some double inequalities, a few cases of particular kernels, and a large number of examples. For reading this book, readers should hold the basic knowledge of Real Analysis. This book is suited to the people who are interested in the field of Analysis inequalities. The author expects this book can help readers to make good progresses in research for Hilbert-type inequalities.