| 1. |
- Aleman, Alexandru, et al.
(författare)
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Estimates in Möbius invariant spaces of analytic functions.
- 2004
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Ingår i: Complex Variables, Theory & Application. - 1563-5066. ; 49:7-9, s. 487-510
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Tidskriftsartikel (refereegranskat)abstract
- We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space. BMOA, the Dirichlet spaces and their recent generalizations ${Cal Q}_K$, which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in $L^p$-spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those ${Cal Q}_K$ spaces which are contained in the Nevanlinna class.
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| 2. |
- Björn, Anders
(författare)
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Removable singularities for hardy spaces
- 1998
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 35:1, s. 1-25
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study removable singularities for Hardy spaces of analytic funtions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A Hejhal For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for the special cases of singularities lying on curves and singularities being self-similar Cantor sets, which the author deals with in other papers. Among the results is the non-removability for Hp of sets with dimension greater than ρ. 0 < ρ < 1. Many counterexamples are provided and the Hp capacities are introduced and studied.
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| 3. |
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| 4. |
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| 5. |
- Kuznetsova, Olga S., et al.
(författare)
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Ullemar’s formula for the Jacobian of the complex moment mapping
- 2004
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Ingår i: Complex Variables, Theory & Application. - : Informa UK Limited. - 0278-1077 .- 1563-5066. ; 49:1, s. 55-72
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Tidskriftsartikel (refereegranskat)abstract
- We prove a formula for the Jacobian of the harmonic moment mapping conjectured earlier by Carina Ullemar.
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| 6. |
- Porten, Egmont
(författare)
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On generalized tube domains over C^n
- 2005
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Ingår i: Complex Variables, Theory & Application. - : Informa UK Limited. - 0278-1077 .- 1563-5066. ; 50:1, s. 1-5
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Tidskriftsartikel (refereegranskat)abstract
- If j : Xj !Rn, j ¼ 1, 2, are domains over Rn, then ¼ X1 X2 carries a canonical structure of a generalized tube domain over Cn. In response to a question of Jarnicki and Pflug (M. Jarnicki and P. Pflug (2000). Extension of Holomorphic Functions, Springer-Verlag), we show that is one-sheeted and equivalent to a product of convex domains, if it is pseudoconvex.
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| 7. |
- Porten, Egmont
(författare)
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On the Hartogs-phenomenon and extension of analytic hypersurfaces in non-separated Riemann domains
- 2002
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Ingår i: Complex Variables, Theory & Application. - : Informa UK Limited. - 0278-1077 .- 1563-5066. ; 47:4, s. 325-332
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper, we answer two questions raised by Jarnicki and Pflug: First, we show by a counterexample that the Hartogs-Bochner theorem is no longer true for non-separated Riemann domains. Secondly, we generalize a structure theorem of Dloussky, which examines the extension of singularity sets contained in analytic hypersurfaces, to non-separated Riemann domains. Moreover, our method yields a new proof of Dloussky's original result.
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| 8. |
- Wikström, Frank
(författare)
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Partial harmonicity of continuous maximal plurisubharmonic functions
- 2002
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933. ; 47:1, s. 73-79
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Tidskriftsartikel (refereegranskat)abstract
- If $u$ is a sufficiently smooth maximal plurisubharmonic function such that the complex Hessian of $u$ has constant rank, it is known that there exists a foliation by complex manifolds, such that $u$ is harmonic along the leaves of the foliation. In this paper, we show a partial analogue of this result for maximal plurisubharmonic functions that are merely continuous, without the assumption on the complex Hessian. In this setting, we cannot expect a foliation by complex manifolds, but we prove the existence of positive currents of bidimension $(1,1)$ such that the function is harmonic along the currents.
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