Geodesic
Descriptions of exceptional sets in the circles for functions from the Bergman space
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 633-649 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $D$ be a domain in $\mathbb{C}^2$. For $w \in \mathbb{C} $, let $D_w = \lbrace z \in \mathbb{C} \mid (z,w) \in D \rbrace $. If $f$ is a holomorphic and square-integrable function in $D$, then the set $E(D,f)$ of all $w$ such that $f(.,w)$ is not square-integrable in $D_w$ is of measure zero. We call this set the exceptional set for $f$. In this note we prove that for every $0
Let $D$ be a domain in $\mathbb{C}^2$. For $w \in \mathbb{C} $, let $D_w = \lbrace z \in \mathbb{C} \mid (z,w) \in D \rbrace $. If $f$ is a holomorphic and square-integrable function in $D$, then the set $E(D,f)$ of all $w$ such that $f(.,w)$ is not square-integrable in $D_w$ is of measure zero. We call this set the exceptional set for $f$. In this note we prove that for every $0$,and every $G_\delta $-subset $E$ of the circle $C(0,r) = \lbrace z \in \mathbb{C} \mid | z | =r \rbrace $,there exists a holomorphic square-integrable function $f$ in the unit ball $B$ in $\mathbb{C}^2$ such that $E(B,f) = E.$
Classification : 32A37, 32H10, 32H99 
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     author = {Jak\'obczak, Piotr},
     title = {Descriptions of exceptional sets in the circles for functions from the {Bergman} space},
     journal = {Czechoslovak Mathematical Journal},
     pages = {633--649},
     year = {1997},
     volume = {47},
     number = {4},
     mrnumber = {1479310},
     zbl = {0901.32006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1997_47_4_a5/}
}
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Jakóbczak, Piotr. Descriptions of exceptional sets in the circles for functions from the Bergman space. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 633-649. http://geodesic.mathdoc.fr/item/CMJ_1997_47_4_a5/

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