Inclusion operators in Bergman spaces on bounded symmetric domains in
We prove that every singular algebraic curve in ℝⁿ admits local tangential Markov inequalities at each of its points. More precisely, we show that the Markov exponent at a point of a real algebraic curve A is less than or equal to twice the multiplicity of the smallest complex algebraic curve containing A.
The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.
A description of bounded pseudoconvex Reinhardt domains, which are complete with respect to the inner -th Carathéodory-Reiffen distance, is given.
2000 Mathematics Subject Classification: Primary 32F45.We present the Carathéodory and the inner Caratheodory distances and the Carathéodory-Reiffen metric on generalized Neil parabolas in Cn. It is a generalization of the results from [4] and [5].This work is a part of the Research Grant No. 1 PO3A 005 28, which is supported by public means in the programme promoting science in Poland in the years 2005–2008.
The purpose of this paper is to present a concise survey of the main properties of biholomorphically invariant pluricomplex Green functions and to describe a number of new examples of such functions. A concept of pluricomplex geodesics is also discussed.
A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.