Relations of the spaces Ap (Ω) and C p (∂Ω)
dc.creator | Georgakopoulos, N | |
dc.creator | Mastrantonis, V | |
dc.creator | Nestoridis, V | |
dc.date.accessioned | 2018-03-14 | |
dc.date.accessioned | 2018-11-24T23:21:23Z | |
dc.date.available | 2018-03-28T10:19:51Z | |
dc.date.available | 2018-11-24T23:21:23Z | |
dc.identifier | https://www.repository.cam.ac.uk/handle/1810/274446 | |
dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3726 | |
dc.description.abstract | Let Ω be a Jordan domain in C, J an open arc of ∂Ω and φ : D → Ω a Riemann map from the open unit disk D onto Ω. Under certain assumptions on φ we prove that if a holomorphic function f ∈ H(Ω) extends continuously on Ω ∪ J and p ∈ {1, 2, . . . } ∪ {∞}, then the following equivalence holds: the derivatives f (l) , 1 ≤ l ≤ p, l ∈ N, extend continuously on Ω ∪ J if and only if the function f|J has continuous derivatives on J with respect to the position of orders l, 1 ≤ l ≤ p, l ∈ N. Moreover, we show that for the relevant function spaces, the topology induced by the l−derivatives on Ω, 0 ≤ l ≤ p, l ∈ N, coincides with the topology induced by the same derivatives taken with respect to the position on J. | |
dc.language | en | |
dc.publisher | Springer | |
dc.publisher | Results in Mathematics | |
dc.subject | Riemann map | |
dc.subject | Poisson Kernel | |
dc.subject | Jordan curve | |
dc.subject | Smoothness on the boundary | |
dc.title | Relations of the spaces Ap (Ω) and C p (∂Ω) | |
dc.type | Article |
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