1,721,013 research outputs found
Topics in dyadic Dirichlet spaces
No full textThe articole investigates the function theory on function spaces on a dyadic tree which model Dirichlet spaces of holomorphic functions. Most of the specific questions addressed deal with Carleson measures on those spaces
Invariance of capacity under quasisymmetric maps of the circle: an easy proof
No full textA combinatorial proof of the invariance of capacity under quasisymmetric maps of the unit circle is given
Some problems on Carleson measures for Besov-Sobolev spaces
No full textWe present some open problems concerning Carleson measures for Besov-Sobolov spaces
Distance Functions for Reproducing Kernel Hilbert Spaces
No full textSuppose is a space of functions on . If is a Hilbert space with reproducing kernel then that structure of can be used to build distance functions on . We describe some of those and their interpretations and interrelations. We also present some computational properties and examples
Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces
Full text linkWe investigate connections between potential theories
on a Ahlfors-regular metric space , on a graph associated with , and on the
tree obtained by removing the ``horizontal edges'' in . Applications to the calculation
of set capacity are given
The Characterization of the Carleson Measures for Analytic Besov Spaces: A Simple Proof
No full textWe give a short proof of an enhanced version of the theorem characterizing the Carleson mesures for the weighted analytic Besov spaces
Carleson measures for the Drury–Arveson Hardy space and other Besov–Sobolev spaces on complex balls
No full textAbstractFor 0⩽σ<1/2 we characterize Carleson measures μ for the analytic Besov–Sobolev spaces B2σ on the unit ball Bn in Cn by the discrete tree condition∑β⩾α[2σd(β)I*μ(β)]2⩽CI*μ(α)<∞,α∈Tn, on the associated Bergman tree Tn. Combined with recent results about interpolating sequences this leads, for this range of σ, to a characterization of universal interpolating sequences for B2σ and also for its multiplier algebra.However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury–Arveson Hardy space Hn2=B21/2. We show that μ is a Carleson measure for B21/2 if and only if both the simple condition2d(α)I*μ(α)⩽C,α∈Tn, and the split tree condition∑k⩾0∑γ⩾α2d(γ)−k∑(δ,δ′)∈G(k)(γ)I*μ(δ)I*μ(δ′)⩽CI*μ(α),α∈Tn, hold. This gives a sharp estimate for Drury's generalization of von Neumann's operator inequality to the complex ball, and also provides a universal characterization of Carleson measures, up to dimensional constants, for Hilbert spaces with a complete continuous Nevanlinna–Pick kernel function.We give a detailed analysis of the split tree condition for measures supported on embedded two manifolds and we find that in some generic cases the condition simplifies. We also establish a connection between function spaces on embedded two manifolds and Hardy spaces of plane domains
Capacity, Carleson measures, boundary convergence, and exceptional sets
No full textIn this paper the relation between certain "testing conditions" and "capacitary conditions" for a measure to be Carleson for the Dirichlet space are discussed, in the dyadic case. In particular, a direct proof of the equivalence of the two conditions is proved, answering a question by Maz'ya.
The analysis of these conditions is then used to give a new definition of capacity and to investigate the boundary behavior of functions in the Dirichlet class
Function spaces related to the Dirichlet space
No full textWe introduce two spaces of holomorphic functions on the disk that play a role in the Dirichlet
space theory similar to the roles of H 1 and BMO in the classical Hardy space theory. We develop
some basic function- and operator-theoretic results for those spaces
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