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arXiv · 1701.05807

Lacunary Müntz spaces: isomorphisms and Carleson embeddings

Loic Gaillard·Pascal Lefèvre
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Abstract

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.

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Loic Gaillard, Pascal Lefèvre. 2017-01-20. Lacunary Müntz spaces: isomorphisms and Carleson embeddings. https://arxiv.org/abs/1701.05807

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