Two more counterexamples to the infinite dimensional Carleson embedding theorem

Abstract

The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.

24 pages

References in corpus (1)

• Vectorial Hankel operators, Carleson embeddings, and notions of $BMOA$

Cited by in corpus (1)

• Vectorial Hankel operators, Carleson embeddings, and notions of $BMOA$