Some refinements and generalizations of Carleman's inequality.
Some remarks about a notion of rearrangement
Some remarks on a paper by A. McD. Mercer: “Polynomials and convex sequence inequalities” [JIPAM. J. Inequal. Pure Appl. Math. 6, 2005, no. 1, Paper No. 8, 4p., electronic only].
Some remarks on Hadamard's inequalities for convex functions.
Some Remarks on Inequalities of Landau and Kolmogorov.
Some remarks on results of Mortici
Some results on a generalized useful information measure.
Some retarded nonlinear integral inequalities in two variables and applications.
Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces.
Some sharp inequalities for Dirac type operators.
Some sharp Simpson type inequalities and applications.
Some sublinear dynamic integral inequalities on time scales.
Some subordination criteria concerning the Sǎlǎgean operator.
Some weighted Hardy-type inequalities on anisotropic Heisenberg groups.
Some weighted multidimensional Berwald, Thunsdorff and Borell inequalities.
Some weighted sum and product inequalities in spaces and their applications.
Spaces defined by the level function and their duals
The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of . These domains are shown to be Banach spaces which, although closely tied to spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
Spectral inequalities involving the sums and products of functions.
Spectral study of a self-adjoint operator on related with a Poincaré type constant
Squaring a reverse AM-GM inequality
Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.