Lacunary Müntz spaces: isomorphisms and Carleson embeddings
In this paper we prove that $M^p_Λ$ is almost isometric to $\ell^p$ in the canonical way when $Λ$ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for Müntz spaces $M^p_Λ$ when $Λ$ is lacunary. We give some necessary and some sufficient conditions to ensure that a Carleson embedding is bounded or compact. In the hilbertian case, the membership to Schatten classes is also studied. When $Λ$ behaves like a geometric sequence the results are sharp, and we get some characterizations.
math.FA↗