Convergence of Poisson integrals on generalized upper half-planes

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Vitali Convergence Theorem for Upper Integrals

It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Convergence of poisson integrals for bounded symmetric domains.

1. The purpose of this note is to describe the extension of the almost everywhere convergence of Poisson integrals to the case of the bounded symmetric domains of Cartan. It is useful to realize such a bounded symmetric domain D as a generalized upper half-plane (i.e., a Siegel domain of type II), and this is done as follows. Let V1 and V2 be two finite-dimensional vector spaces over C. Assume ...

Realization of Hermitian Symmetric Spaces as Generalized Half-planes