Weak and strong limit values
Complex Variables
2012-10-04 v2
Abstract
The classical results about the boundary values of holomorphic or harmonic functions on a domain state that under additional integrability assumptions these functions have limits along specific sets approaching boundary. The proofs of these results are based on properties of smooth boundaries used to define the approach regions and on estimates of representing kernels along these regions. This paper attempts to look at the situation when no assumptions about the boundary smoothness are made and, consequently, no natural definitions of approach regions could be given.
Cite
@article{arxiv.1105.1365,
title = {Weak and strong limit values},
author = {Evgeny A. Poletsky},
journal= {arXiv preprint arXiv:1105.1365},
year = {2012}
}