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.
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Nicola Arcozzi, Richard Rochberg, Eric T. Sawyer, Carleson measures for analytic Besov spaces. Rev. Mat. Iberoam. 18 (2002), no. 2, pp. 443–510DOI 10.4171/RMI/326