Half-discrete Hilbert-type Inequalities

1. Recent developments of Hilbert-Type inequalities with applications. 1.1. Introduction. 1.2. Hilbert's inequality and Hilbert's operator. 1.3. Modern research for Hilbert-type inequalities. 1.4. Some new applications for Hilbert-type inequalities. 1.5. Concluding remarks -- 2. Improvements of the Euler-Maclaurin summation formula and applications. 2.1. Introduction. 2.2. Some special functions relating Euler-Maclaurin's summation formula. 2.3. Estimations of the residue term about a class series. 2.4. Two classes of series estimations -- 3. A half-discrete Hilbert-type inequality with a general homogeneous kernel. 3.1. Introduction. 3.2. Some preliminary lemmas. 3.3. Some theorems and corollaries -- 4. A half-discrete Hilbert-type inequality with a non-homogeneous kernel. 4.1. Introduction. 4.2. Some preliminary lemmas. 4.3. Some theorems and corollaries. 4.4. Some particular examples -- 5. Multi-dimensional half-discrete Hilbert-type inequalities. 5.1. Introduction. 5.2. Some preliminary results and lemmas. 5.3. Some inequalities related to a general homogeneous kernel. 5.4. Some inequalities relating a general non-homogeneous kernel -- 6. Multiple half-discrete Hilbert-type inequalities. 6.1. Introduction. 6.2. First kind of multiple Hilbert-type inequalities. 6.3. Second kind of multiple Hilbert-type inequalities. 6.4. Some examples with the particular kernels

Author: Bicheng Yang, Lokenath Debnath

Publisher: World Scientific Publishing Company Incorporated

Publication Date: Feb 19, 2014

Number of Pages: 333 pages

Language: English

Binding: Hardcover

ISBN-10: 9814504971

ISBN-13: 9789814504973