Recent Developments of Hilbert-Type Inequalities with Applications

The following sections are included:

• Introduction

• Hilbert's Inequality and Hilbert's Operator

  • Hilbert's Discrete and Integral Inequalities

  • Operator Formulation of Hilbert's Inequality

  • A More Accurate Discrete Hilbert's Inequality

  • Hilbert's Inequality with One Pair of Conjugate Exponents

  • A Hilbert-type Inequality with the General Homogeneous Kernel of Degree −1

  • Two Multiple Hilbert-type Inequalities with the Homogeneous Kernels of Degree (−n+1)

• Modern Research for Hilbert-type Inequalities

  • Modern Research for Hilbert's Integral Inequality

  • On the Way of Weight Coefficient for Giving a Strengthened Version of Hilbert's Inequality

  • Hilbert's Inequality with Independent Parameters

  • Hilbert-type Inequalities with Multi-parameters

• Some New Applications for Hilbert-type Inequalities

  • Operator Expressions of Hilbert-type Inequalities

  • Some Basic Hilbert-type Inequalities

  • Some Applications to Half-discrete Hilbert-type Inequalities

• Concluding Remarks