Hilbert integral operator inequalities

Some Integral Inequalities Related to Hilbert ’

We prove some integral inequalities involving the Laplace transform. These are sharper than some known generalizations of the Hilbert integral inequality including a recent result of Yang.

Hilbert–pachpatte Type Multidimensional Integral Inequalities

In this paper we use a new approach to obtain a class of multivariable integral inequalities of Hilbert type from which we can recover as special cases integral inequalities obtained recently by Pachpatte and the present authors.

Sharper Inequalities for Numerical Radius for Hilbert Space Operator

We give several sharp inequalities for the numerical radius of Hilbert space operators .It is shown that if A and B are bounded linear operators on complex Hilbert space H , then 1 2 1 2(1 ) 2(1 ) 2 2 2 2 1 ( ) 2 ( ) 2 r r r r r r w A B A B A B A B α α α α − − − ∗ ∗ ⎛ ⎞ + ≤ + + + + + ⎜ ⎟ ⎝ ⎠ , for 0<r 1 ≤ and ( ) 1 , 0 ∈ α , and if ( ) n A M ∈ , then 2 1 ( ) 4 w A ≤ ( ) 2 2 A A A A ∗ ∗ + + − , ...

Some Refinements of Hilbert-pachpatte Type Integral Inequalities

In this paper, we obtain an extension of a multivariable integral inequality of Hilbert-Pachpatte type. By specializing the upper estimate functions in the hypothesis and the parameters, we obtain many special cases.

On a Multiple Hilbert-Type Integral Operator and Applications