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We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disk having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson balayage. We deduce necessary and sufficient geometric conditions, both expressed in terms of certain maximal functions. 相似文献
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E. S. Dubtsov 《Journal of Mathematical Sciences》2007,141(5):1531-1537
Let
and τ denote the invariant gradient and invariant measure on the unit ball B of ℂn, respectively. Assume that f is a holomorphic function on B and ϕ ∈ C2(ℝ) is a nonnegative, nondecreasing, convex function. Then f belongs to the Hardy-Orlicz space H
ϕ(B>) if and only if
Analogous characterizations of Bergman-Orlicz spaces are obtained. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 43–53. 相似文献
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Shinji Yamashita 《Israel Journal of Mathematics》1981,39(3):259-264
Letf be a function holomorphic inU={|z|<1}, and letA(R,f) be the area off(U)∩{|w|<R}, not counting multiplicities. IfA(R,f)=O(R
γ) asR→∞ for a γ, 0≦γ<2, then the subharmonic function exp |f|
p
has a harmonic majorant inU for eachp, 0<p<2−γ. If 0≦γ<1 further, thene
f
is of Hardy classH
p
for eachp, 0<p<∞. 相似文献
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J. Heber 《Geometric And Functional Analysis》2006,16(4):869-890
We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric
Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of
nonpositive sectional curvatures [N2].
Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154).
Received: September 2004; Revision: June 2005; Accepted: September 2005 相似文献
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We consider interpolation of discrete functions by continuous ones with restriction on the size of spectra. We discuss a sharp contrast between the cases of compact and unbounded spectra. In particular we construct ‘universal’ spectra of small measure which deliver positive solution of the interpolation problem in Bernstein spaces for every discrete sequence of knots. 相似文献
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The interpolation problem for a reflexive algebra Alg is this: Given two operators and , under what conditions can we be sure that there will exist an operator in Alg such that ? There are simple necessary conditions that have been investigated in several earlier papers. Here we present an example to show that the conditions are not, in general, sufficient. We also suggest a strengthened set of conditions which are necessary and are ``almost' sufficient, in the sense that they will ensure that lies in the weak-operator closure of the set {:Alg}.
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In this paper we present an interpolation inequality in the homogeneous Besov spaces on , which reduces to a number of well-known inequalities in special cases.
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Recently Korevaar and Schoen developed a Sobolev theory for maps from smooth (at least ) manifolds into general metric spaces by proving that the weak limit of appropriate average difference quotients is well
behaved. Here we extend this theory to functions defined over Lipschitz manifold. As an application we then prove an existence
theorem for harmonic maps from Lipschitz manifolds to NPC metric spaces.
Received December 6, 1996 / Accepted March 4, 1997 相似文献
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