On discrete subspaces of a Hilbert space
Consider a family of integral operators and a related family of differential operators, both defined on a class of analytic functions holomorphic in the unit disk, distortion properties of the real part are derived from a general aspect.
A complete isomorphic classification is obtained for Köthe spaces such that ; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and . Any of these spaces has the quasi-equivalence property.
We give a description of the dual of a Calderón-Lozanovskiĭ intermediate space φ(X,Y) of a couple of Banach Köthe function spaces as an intermediate space ψ(X*,Y*) of the duals, associated with a "variable" function ψ.
Several conditions are given under which l1 embeds as a complemented subspace of a Banach space E if it embeds as a complemented subspace of an Orlicz space of E-valued functions. Previous results in Pisier (1978) and Bombal (1987) are extended in this way.
This paper is devoted to embedding theorems for classes of functions of several variables. One of our main objectives is to give an analysis of some basic embeddings as well as to study relations between them. We also discuss some methods in this theory that were developed in the last decades. These methods are based on non-increasing rearrangements of functions, iterated rearrangements, estimates of sections of functions, related mixed norms, and molecular decompositions.