Abstract
In this chapter, we build some Hilbert-type integral inequalities with two pairs of conjugate exponents and an independent parameter, and consider their operator characterizations. The equivalent forms and the reverses are also given. Some sufficient conditions of bounded operator are established and a number of particular inequalities are deduced. The proofs of some basic theorems are used the limit theorems in the theory of Lebesgue integrals and the technique of real analysis.
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Advanced Calculus - Fundamentals of Mathematics
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
An Introduction to Sobolev Spaces
An Introduction to Trigonometry and its Applications
Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods
Applied Computational Mathematics in Social Sciences
Calculus: The Logical Extension of Arithmetic
Complex Analyses in Engineering, Science and Technology
Convergence Theorems for Lattice Group-Valued Measures