In this book, the author considers several extended applications of the well-known half-discrete Hardy-Hilbert’s inequality with two internal variables, by using the techniques of real analysis, the way of introduced parameters and the weight function. The book first considers the basic results of half-discrete Hardy-Hilbert’s inequality. Then it obtains some new inequalities involving upper limit functions, derivative functions and partial sums, and studies the equivalent conditions of the best possible constant factors related to the parameters by 8 chapters. The author constructs a large kind of half-discrete Hardy-Hilbert’s inequalities for building their extended applications. The lemmas and theorems in this book provide an extensive account of this kind of inequalities and applications. This book will be helpful to researchers who are interested in half-discrete Hardy-Hilbert’s inequality.
