Norm and Taylor coefficients estimates of holomorphic functions in balls

Jacob Burbeam; Do Young Kwak

Annales Polonici Mathematici, Tome 55 (1991), p. 271-297 / Harvested from The Polish Digital Mathematics Library

Résumé

A classical result of Hardy and Littlewood states that if $f (z) = \sum_{m = 0}^{\infty} a_{m} z^{m}$ is in $H^{p}$ , 0 < p ≤ 2, of the unit disk of ℂ, then $\sum_{m = 0}^{\infty} {(m + 1)}^{p - 2} {| a_{m} |}^{p} \leq c_{p} ∥ f ∥_{p}^{p}$ where $c_{p}$ is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of $ℂ^{n}$ , and use this extension to study some related multiplier problems in $ℂ^{n}$ .

Publié le : 1991-01-01

Zbl 0743.32006

EUDML-ID : urn:eudml:doc:262478

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     author = {Jacob Burbeam and Do Young Kwak},
     title = {Norm and Taylor coefficients estimates of holomorphic functions in balls},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {271-297},
     zbl = {0743.32006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p271bwm}
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Jacob Burbeam; Do Young Kwak. Norm and Taylor coefficients estimates of holomorphic functions in balls. Annales Polonici Mathematici, Tome 55 (1991) pp. 271-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p271bwm/

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