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We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.
Dans cet article, nous démontrons une inégalité liant la croissance d’un casoratien généralisé de séries entières -adique à la croissance du casoratien ordinaire de ces séries entières. Il en résulte que si le casoratien de fonctions entières -adiques est un polynôme non nul, alors toutes ces fonctions sont des polynômes. Comme application, nous montrons que si une équation aux différences linéaire d’ordre à coefficients dans a solutions méromorphes dans tout , linéairement indépendantes...
We show how certain geometric conditions on a planar set imply that the set must lie on a quasicircle, and we give a geometric characterization of all subsets of the plane that are quasiconformally equivalent to the usual Cantor middle-third set.
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