Abstract
We give a characterization of Carleson measures for diagonal Besov spaces of martingales on homogeneous trees by means of testing type conditions. The corresponding problem for spaces harmonic functions in the unit ball was solved by means of a capacitary condition in (Guliyev, Wu in Further Progress in Analysis, pp. 132–141 (1999)). For a given measure, however, capacitary conditions are more difficult to verify than testing conditions. The problem of characterizing Carleson measures for Besov spaces of harmonic functions by means of testing conditions is still open.
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