Embedding theorems for Müntz spaces
Annales de l'Institut Fourier, Volume 61 (2011) no. 6, p. 2291-2311
We discuss boundedness and compactness properties of the embedding M Λ 1 L 1 (μ), where M Λ 1 is the closed linear span of the monomials x λ n in L 1 ([0,1]) and μ is a finite positive Borel measure on the interval [0,1]. In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences Λ. Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from M Λ 1 to L 1 ([0,1]).
Nous étudions la continuité et la compacité du plongement M Λ 1 L 1 (μ), où M Λ 1 est l’enveloppe linéaire fermée des monômes x λ n dans L 1 ([0,1]) et où μ est une mesure borélienne positive et finie sur [0,1]. En particulier, nous introduisons une classe de mesures “sous-linéaires” et nous donnons une solution complète au problème de plongement pour une classe de suites quasilacunaires Λ. Finalement nous montrons comment retrouver des résultats de Al Alam concernant la continuité et la norme essentielle des opérateurs de composition à poids de M Λ 1 dans L 1 ([0,1]).
DOI : https://doi.org/10.5802/aif.2674
Classification:  46E15,  47A30,  47B33
Keywords: Müntz space, embedding measure, weighted composition operator, compact operator, essential norm
@article{AIF_2011__61_6_2291_0,
     author = {Chalendar, Isabelle and Fricain, Emmanuel and Timotin, Dan},
     title = {Embedding theorems for M\"untz spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     pages = {2291-2311},
     doi = {10.5802/aif.2674},
     mrnumber = {2976312},
     zbl = {1255.46013},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_6_2291_0}
}
Chalendar, Isabelle; Fricain, Emmanuel; Timotin, Dan. Embedding theorems for Müntz spaces. Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2291-2311. doi : 10.5802/aif.2674. http://www.numdam.org/item/AIF_2011__61_6_2291_0/

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