Lacunary Müntz spaces: isomorphisms and Carleson embeddings
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, p. 2215-2251
In this paper we prove that M Λ p is almost isometric to 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 Λ p when Λ is lacunary. We give some necessary and some sufficient conditions ensuring 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.
Dans cet article, nous montrons que M Λ p est presque isométrique à p , et ce de façon naturelle, lorsque Λ est lacunaire avec une raison grande. Par ailleurs, notre approche permet aussi d’étudier les mesures de Carleson pour les espaces Müntz M Λ p lorsque Λ est lacunaire. Nous donnons des conditions nécessaires et des conditions suffisantes qui permettent d’assurer qu’un plongement de Carleson est borné ou compact. Dans le cadre hilbertien, nous étudions aussi l’appartenance de ce plongement aux classes de Schatten. Nous obtenons des caractérisations complètes lorsque Λ se comporte comme une suite géométrique.
Received : 2017-01-17
Revised : 2017-07-22
Accepted : 2017-11-07
Published online : 2018-11-23
Classification:  30B10,  47B10,  47B38
Keywords: Müntz spaces, Carleson embeddings, lacunary sequences, Schatten classes
     author = {Gaillard, Lo\"\i c and Lef\`evre, Pascal},
     title = {Lacunary M\"untz spaces: isomorphisms and Carleson embeddings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     pages = {2215-2251},
     doi = {10.5802/aif.3207},
     language = {en},
     url = {}
Lacunary Müntz spaces: isomorphisms and Carleson embeddings. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2215-2251. doi : 10.5802/aif.3207.

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