9 research outputs found
Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains
We characterize using the Bergman kernel Carleson measures of Bergman spaces
in strongly pseudoconvex bounded domains in several complex variables,
generalizing to this setting theorems proved by Duren and Weir for the unit
ball. We also show that uniformly discrete (with respect to the Kobayashi
distance) sequences give examples of Carleson measures, and we compute the
speed of escape to the boundary of uniformly discrete sequences in strongly
pseudoconvex domains, generalizing results obtained in the unit ball by
Jevti\'c, Massaneda and Thomas, by Duren and Weir, and by MacCluer.Comment: 17 page
Discrete sequences in unbounded domains
Discrete sequences with respect to the Kobayashi distance in a strongly
pseudoconvex bounded domain are related to Carleson measures by a formula
that uses the Euclidean distance from the boundary of .
Thus the speed of escape at the boundary of such sequence has been studied in
details for strongly pseudoconvex bounded domain .
In this note we show that such estimations completely fail if the domain is
not bounded.Comment: 4 page