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FINELY HOLOMORPHIC-FUNCTIONS

Abstract:

Let O(U) denote the finely harmonic functions on U a finely open subset of C such that ∂g ∂ z ̄ = 0 almost surely on U. Define Af(K) to be those g in C(K) such that if K′ is the fine interior of K then g |K′ is in O(K). We prove that Af(K) is invariant under the Vitushkin localization operators, i.e., it is T-invariant. We also settle an open question of Fuglede on the existence of polygonal arcs in finely open subsets of Rn. Using T-invariance we prove that point derivation yields a continuo...

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Publication status:
Published

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Journal:
JOURNAL OF FUNCTIONAL ANALYSIS
Volume:
37
Issue:
1
Pages:
1-18
Publication date:
1980
DOI:
EISSN:
1096-0783
ISSN:
0022-1236
URN:
uuid:6d1bba3b-527b-49c3-9fa8-c5c1d8b58b0f
Source identifiers:
4515
Local pid:
pubs:4515
Language:
English

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