On Shafer and Carlson Inequalities

On Shafer and Carlson Inequalities

Optimal recovery of operators and multidimensional Carlson type inequalities

1. General setting Let T be a nonempty set, Σ be the σ -algebra of subsets of T , and μ be a nonnegative σ -additive measure on Σ . We denote by Lp(T , Σ, μ) (or simply Lp(T , μ)) the set of all Σ-measurable functions with values in R or in C for which ∥x(·)∥Lp(T ,μ) =  T |x(t)|p dμ(t) 1/p < ∞, 1 ≤ p < ∞, ∥x(·)∥L∞(T ,μ) = ess sup t∈T |x(t)| < ∞, p = ∞. Put W = {x(·) ∈ Lp(T , μ) : ∥φ(·)x(·)∥L...

One-dimensional Interpolation Inequalities, Carlson–landau Inequalities and Magnetic Schrödinger Operators

In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson–Landau-type inequalities and to magnetic Schrödinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrödinger operators on multi-dimensional cylinders.

Commentary on Hunt and Carlson (2007)

‘‘Research on group differences in intelligence is scientifically valid and socially important’’ (Hunt & Carlson, 2007, this issue, p. 195). Hunt and Carlson are to be commended not only for standing up for the legitimacy of such research but also for reporting basic facts on the science that others outside the field often deny or distort. Among the much-replicated empirical findings that Hunt ...

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine