On Some Improvement And Extension Of Hardy-Hilbert Type Inequalities

Hilbert type inequalities are important inequalities in analysis.In this pa-per,by introducing appropriate weight functions and parameterization methods,for the improvement and promotion of the half-discrete and multiple integral Hardy-Hilbert type inequalities,building more optimized inequalities in the whole plane.The equivalent form and the reverses are given,the operator rep-resentation and some special results are considered,and the optimal property of the constant factor is proved.Chapter 1:The background,significance and main conclusions of this paper are introduced.Chapter 2:By the use of weight functions and technique of real analysis,a new half-discrete Hilbert-type inequality in the whole plane with multiparame-ters and the best possible constant factor is given.Furthermore,the equivalent forms,two kinds of particular inequalities,and the operator expressions with the norm are considered.Chapter 3:By introducing some interval variables and using weight func-tions and real analysis,a multiple Hilbert-type integral inequality in the whole space with a best possible constant factor is given,which is an extension of some published results.The equivalent forms,the operator expressions with the norm,the reverses,a few particular cases and some examples with particu-lar kernels are also considered.Chapter 4:By means of the way of the weight functions,the technique of real analysis and the improved Holders inequality,a discrete Mulholland type inequality with parameters and a half-discrete Hilbert inequality are strength-ened.Then some new inequalities are given.Chapter 5:We summarize the content and prospect the future research.