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Relations of the spaces Ap (Ω) and C p (∂Ω)

dc.creatorGeorgakopoulos, N
dc.creatorMastrantonis, V
dc.creatorNestoridis, V
dc.description.abstractLet 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.publisherResults in Mathematics
dc.subjectRiemann map
dc.subjectPoisson Kernel
dc.subjectJordan curve
dc.subjectSmoothness on the boundary
dc.titleRelations of the spaces Ap (Ω) and C p (∂Ω)

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