Lacunary Müntz spaces: isomorphisms and Carleson embeddings

2017/01/20 by Gaillard, Loic, Lefèvre, Pascal · 2 citations
#30B10 #47B10 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1701.05807

Abstract

In this paper we prove that M^p_Λ is almost isometric to ℓ^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.

Cited by

• On Markushevich bases \x^λ_n\_n=1^∞ for their closed span in weighted L² (A) spaces over sets A⊂ [0,∞) of positive Lebesgue measure, hereditary completeness, and moment problems
• On Strong Markushevich bases \t^λ_n\_n=1^∞ in their closed span in L² (0, 1) and characterizing a subspace of H² (\mathbbD)

Related

• Generalized Carleson Embeddings of Müntz Spaces
• Carleson-type embeddings with closed range
• Two properties of Müntz spaces
• Interpolation Between H^p Spaces and Non-Commutative Generalizations II
• L²-Müntz spaces as model spaces