Geodesic
Norm and Taylor coefficients estimates of holomorphic functions in balls
Annales Polonici Mathematici, Tome 54 (1991) no. 3, pp. 271-297.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A classical result of Hardy and Littlewood states that if $f(z) = ∑_{m=0}^{∞} a_m z^m$ is in $H^p$, 0 p ≤ 2, of the unit disk of ℂ, then $∑_{m=0}^{∞} (m+1)^{p-2}|a_m|^p ≤ c_p ∥f∥_p^p$ 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 $ℂ^n$.
DOI : 10.4064/ap-54-3-271-297

Jacob Burbeam 1 ; Do Kwak 1

1 
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Jacob Burbeam; Do Kwak. Norm and Taylor coefficients estimates of holomorphic functions in balls. Annales Polonici Mathematici, Tome 54 (1991) no. 3, pp. 271-297. doi : 10.4064/ap-54-3-271-297. http://geodesic.mathdoc.fr/articles/10.4064/ap-54-3-271-297/

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