Journal article
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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- Publisher copy:
- 10.1016/0022-1236(80)90024-5
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Bibliographic Details
- Journal:
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume:
- 37
- Issue:
- 1
- Pages:
- 1-18
- Publication date:
- 1980-01-01
- DOI:
- EISSN:
-
1096-0783
- ISSN:
-
0022-1236
- Source identifiers:
-
4515
Item Description
- Language:
- English
- Pubs id:
-
pubs:4515
- UUID:
-
uuid:6d1bba3b-527b-49c3-9fa8-c5c1d8b58b0f
- Local pid:
- pubs:4515
- Deposit date:
- 2012-12-19
Terms of use
- Copyright date:
- 1980
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