A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities.
A theory on perturbations of the Dirac operator.
A topology on inequalities.
A trilinear restriction problem for the paraboloid in .
A two-sided estimate of .
A two-weight inequality for the Bessel potential operator
Necessary conditions and sufficient conditions are derived in order that Bessel potential operator is bounded from the weighted Lebesgue spaces into when .
A unified approach to several inequalities involving functions and derivatives
There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and -dimensional results are also given.
A unified treatment of some sharp inequalities.
A variance analog of majorization and some associated inequalities.
A variant of a general inequality of the Hardy-Knopp type.
A variant of Jensen's inequality.
A variant of Jensen-Steffensen's inequality for convex and superquadratic functions.
A variant of Jessen's inequality and generalized means.
A variant of Jessen's inequality of Mercer's type for superquadratic functions.
A Volterra inequality with the power type nonlinear kernel.
A weighted estimate for an intermediate operator on the cone of nonnegative functions.
A weighted inequality for derivatives on the half-line.
A weighted inequality for the Hardy operator involving suprema
Let be a weight on . Assume that is continuous on . Let the operator be given at measurable non-negative function on by We characterize weights on for which there exists a positive constant such that the inequality holds for every . Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.
A weighted isoperimetric inequality and applications to symmetrization.
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.