О СЛЕДАХ И ДИСТАНЦИЯХ В АНАЛИТИЧЕСКИХ ФУНКЦИОНАЛЬНЫХ ПРОСТРАНСТВАХ В Cn И ИНТЕГРАЛАХ МАРТИНЕЛЛИ – БОХНЕРА

Abstract

In this note we provide some analogues of our numerous recent results on traces and distances in terms of Martinelly — Bochner integrals and kernels. These are first results of this type in terms of such kernels. Some assertions for Martinelly — Bochner integrals related with Holder classes and Lebegues points will be also discussed. In recent years various new sharp results on traces and distances were provided in a big series of papers of the first author. In all these papers properties of Bergman-type kernels and Bergman-type integral representations are playing a critical role. The intension of this paper to find some analogues of these results in terms of or with the help of more general integral representations and more general kernels in analytic function spaces in higher dimension so-called Martinelly — Bochner integral representations and Martinelly — Bochner kernels in Cn. Our work consists of three parts. In the first part we partially generalize our results on traces. In the second part we provide estimates of distance function in terms of Martinelly — Bochner kernels and Martinelly — Bochner integrals. In the third part we present results on Martinelly — Bochner integrals related with Holder classes and Lebegues points. This type of issues arise naturally in view of recent series of papers and new results of the first author on multifunctional analytic spaces and related issues. In our proofs we modify the methods of earlier results and theorems for the case of Martinelli-Bochner integrals and kernels.