Norm and Taylor coefficients estimates of holomorphic functions in balls
Annales Polonici Mathematici, Tome 54 (1991) no. 3, pp. 271-297
Cet article a éte moissonné depuis 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 $ℂ^n$.
@article{10_4064_ap_54_3_271_297,
author = {Jacob Burbeam and Do Kwak},
title = {Norm and {Taylor} coefficients estimates of holomorphic functions in balls},
journal = {Annales Polonici Mathematici},
pages = {271--297},
year = {1991},
volume = {54},
number = {3},
doi = {10.4064/ap-54-3-271-297},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-54-3-271-297/}
}
TY - JOUR AU - Jacob Burbeam AU - Do Kwak TI - Norm and Taylor coefficients estimates of holomorphic functions in balls JO - Annales Polonici Mathematici PY - 1991 SP - 271 EP - 297 VL - 54 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap-54-3-271-297/ DO - 10.4064/ap-54-3-271-297 LA - en ID - 10_4064_ap_54_3_271_297 ER -
%0 Journal Article %A Jacob Burbeam %A Do Kwak %T Norm and Taylor coefficients estimates of holomorphic functions in balls %J Annales Polonici Mathematici %D 1991 %P 271-297 %V 54 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/ap-54-3-271-297/ %R 10.4064/ap-54-3-271-297 %G en %F 10_4064_ap_54_3_271_297
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
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