منابع مشابه
Harmonic Bergman Functions on Half-spaces
We study harmonic Bergman functions on the upper half-space of Rn. Among our main results are: The Bergman projection is bounded for the range 1 < p <∞; certain nonorthogonal projections are bounded for the range 1 ≤ p < ∞; the dual space of the Bergman L1-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range 1 ≤ p <∞; the Bergma...
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The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n ≥ 2. To this end, we first generalize the Carleman’s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna’s representation for harmonic functions in the half s...
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This note presents elementary geometric descriptions of several simple families of harmonic functions on the upper sheet of the unit hyperboloid in Minkowski three-space. As is briefly discussed here, these calculations grew out of an earlier attempt to construct Poincaré series on punctured surfaces using Minkowski geometry. Introduction The material in this note grew out of an attempt (discus...
متن کاملA special subspace of weighted spaces of holomorphic functions on the upper half plane
In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...
متن کاملEquivariant Vector Bundles on Drinfeld ’ S Upper Half Space Sascha
Let X ⊂ PdK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PdK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H(X ,F). The graded pieces of this filtration are locally analytic in...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2012
ISSN: 1370-1444
DOI: 10.36045/bbms/1353695908