Carlson type inequalities and embeddings of interpolation spaces

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.

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

Interpolation Inequalities in Weighted Sobolev Spaces

In this paper we prove some interpolation inequalities between functions and their derivatives in the class of weighted Sobolev spaces defined on unbounded open subset Ω ⊂ Rn .

Hölder inequalities and sharp embeddings in function spaces of B spq and F s pq type

where in that special case c = 1 may be chosen. With exception of Subsection 1.2, all spaces in this paper are defined on R . This justifies to omit R in the sequel. One of the main aims of the paper is to study the appropriate counterparts of (1.1.1) and (1.1.2) for the spaces B pq and F s pq . That means for a given smoothness s we are looking for B p1q1 B s p2q2 ⊂ B pq (1.1.4) 1991 Mathemati...