Weak and strong limit values

2011/05/06 by Evgeny A. Poletsky, Poletsky, Evgeny A.
Computer Science · Mathematics · #28A33 (Primary) 30E25 #31E20 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Numerical methods in inverse problems #math.CV #msc:28A33 #msc:30E25 #msc:31E20

paper · pdf · doi:10.48550/arxiv.1105.1365

openalex publication_date 2011/05/06 · arxiv created 2012/10/03 · arxiv updated 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical results about the boundary values of holomorphic or harmonic functions on a domain D 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.

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