Geodesic
UNIVERSAL RADIAL LIMITS OF HOLOMORPHIC FUNCTIONS
Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 261-267

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DOI

We investigate the radial behavior of holomorphic functions in the unit ball $B$ of $\mtc^n$. In particular, we prove the existence of universal holomorphic functions $f$ in the following sense : given any measurable function $\vphi$ on $\partial B$, there is a sequence $(r_n)_{n\geq 1}$, $0, that converges to 1, such that $f(r_n\xi)$ converges to $\vphi(\xi)$ for almost every $\xi\,{\in}\,\partial B$.
DOI : 10.1017/S0017089505002478
Mots-clés : 32A40 
BAYART, FRÉDÉRIC. UNIVERSAL RADIAL LIMITS OF HOLOMORPHIC FUNCTIONS. Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 261-267. doi: 10.1017/S0017089505002478
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     author = {BAYART, FR\'ED\'ERIC},
     title = {UNIVERSAL {RADIAL} {LIMITS} {OF} {HOLOMORPHIC} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {261--267},
     year = {2005},
     volume = {47},
     number = {2},
     doi = {10.1017/S0017089505002478},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002478/}
}
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