A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel

The following sections are included:

• Introduction

• Some Preliminary Lemmas

  • Definition of Weight Functions and Related Lemmas

  • Estimations about Two Series

  • Some Inequalities Relating the Constant k(λ₁)

• Some Theorems and Corollaries

  • Equivalent Inequalities and their Operator Expressions

  • Two Classes of Equivalent Reverse Inequalities

  • Some Corollaries

  • Some Particular Examples

  • Applying Condition (iii) and Corollary 3.8

  • Applying Condition (iii) and Corollary 3.4