On Bergman-type spaces in tubular domains over symmetric cones

Some properties of new Bergman-type integral operators on product of the tube domains are obtained. An integral condition in tube to get atomic-type decomposition in multifunctional analytic Bergman spaces in tube domains over symmetric cones are provided.

Recurrence and transience for normally reflected Brownian motion in warped product manifolds

We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by Pinsky, who treated the case in which the ambient space is flat, our result recovers the classical test for the standard Brownian motion in model spaces. Moreover, it allows us to discuss the recurrence/transience dichotomy for certain generalized tube domains around totally geodesic submanifolds in hyperbolic space.