Carlson type 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...

On Shafer and Carlson Inequalities

Some Multiplicative Inequalities for Inner Products and of the Carlson Type

Recommended by Wing-Sum Cheung We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.

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.

On Generalization of Cebysev Type Inequalities

In this paper, we establish new Cebysev type integral inequalities involving functions whose derivatives belong to L_{p} spaces via certain integral identities.