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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 26, Fasc. 1,
pages 155 - 173
 

BESSEL POTENTIALS, GREEN FUNCTIONS AND EXPONENTIAL FUNCTIONALS ON HALF-SPACES

T. Byczkowski
M. Ryznar
H. Byczkowska

Abstract: The purpose of the paper is to provide precise estimates for the Green function corresponding to the operator (I- D)a/2, 0 < a < 2. The potential theory of this operator is based on Bessel potentials J = (I- D) -a/2. a In probabilistic terms it corresponds to a subprobabilistic process obtained from the so-called relativistic a -stable process. We are interested in the theory of the killed process when exiting a fixed half-space. The crucial role in our research is played by (recently found) an explicit form of the Green function of a half-space. We also examine properties of some exponential functionals corresponding to the operator (I- D)a/2.

2000 AMS Mathematics Subject Classification: Primary 60J65; Secondary 60J60.

Key words and phrases: Bessel potentials, Riesz kernels, relativistic process, stable process, Poisson kernel, Green function, half-spaces.

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