This is an announcement for the paper “Lacunary Müntz spaces: isomorphisms and Carleson embeddings” by Loic Gaillardhttps://arxiv.org/find/math/1/au:+Gaillard_L/0/1/0/all/0/1, Pascal Lefèvrehttps://arxiv.org/find/math/1/au:+Lefevre_P/0/1/0/all/0/1.
Abstract: In this paper we prove that $M_{\Lambda}^p$ is almost isometric to $\ell_p$ in the canonical way when $\Lambda$ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for M"untz spaces $M_{\Lambda}^p$ when $\Lambda$ 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 $\Lambda$ behaves like a geometric sequence the results are sharp, and we get some characterizations.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.05807