Pluriharmonic boundary values

Non-tangential and probabilistic boundary behavior of pluriharmonic functions

Let u be a pluriharmonic function on the unit ball in Cn. I consider the relationship between the set of points Lu on the boundary of the ball at which u converges non-tangentially, and the set of points Lu at which u converges along conditioned Brownian paths. For harmonic funcitons u of two variables, the result Lu a.e. = Lu has been known for some time, as has a counterexample to the same eq...

Function Values as Boundary Integrals

Analytic Functions and Boundary Values

Analytic functions in tubes T B = R+iB in C, where B 1⁄2 R, that generalize the Hardy H spaces are studied. The associated function M¤ of Komatsu, which is de ̄ned with the aid of certain sequences of positive real numbers, is involved in the generalizing bound of the L norm. Fourier-Laplace and Cauchy integral representations are obtained for these functions. These representations can be used t...

Commuting Toeplitz Operators with Pluriharmonic Symbols

By making use of M-harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in n-dimensional complex space.

Berezin Transforms on Pluriharmonic Bergman Spaces

We show that, perhaps surprisingly, in several aspects the behaviour of the reproducing kernels, of Toeplitz operators and of the Berezin transform on some weighted pluriharmonic Bergman spaces is the same as in the holomorphic case.