1,721,019 research outputs found
A Comparison Between the Bergman and Szegö Kernels of the Non-smooth Worm Domain D′β
No full textIn this work we provide an asymptotic expansion for the Szegö kernel associated to a suitably defined Hardy space on the non-smooth worm domain D′β. After describing the singularities of the kernel, we compare it with an asymptotic expansion of the Bergman kernel. In particular, we show that the Bergman kernel has the same singularities of the first derivative of the Szegö kernel with respect to any of the variables. On the side, we prove the boundedness of the Bergman projection operator on Sobolev spaces of integer order
On Hardy spaces on worm domains
Full text linkIn this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection
on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded
pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and
we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce
and discuss the results we have obtained so far in the setting of non-smooth worm domains
ON THE REGULARITY OF SINGULAR INTEGRAL OPERATORS ON COMPLEX DOMAINS
Full text linkGiven a doman in , it is a classical problem to study the boundary behavior of functions which are holomorphic on . The boundary values of a given function are often expressed by means of singular integral operators. In this thesis we study this problem in two different settings with different motivations. In the first part we deal with a non-smooth version of the so-called worm domain in order to understand the role played by the pathological geometry of this domain. In the second part we study the problem in the case of a product Lipschitz surface and some boundedness results for biparameter singular integral operators are proved
Ahlfors regular spaces have regular subspaces of any dimension
Full text linkWe characterize Q-dimensional Ahlfors regular spaces among trees’ boundaries and show how to construct, for each 0 < α < Q, an α-regular subspace. As an application, we give an alternative simple proof of the existence of α-regular subspaces of a Q-dimensional complete Ahlfors regular metric space (X, ρ), which was proved in [8]
Adapting Publish-Subscribe Routing to Traffic Demands
No full textMost of currently available content-based publish-subscribe systems that were designed to operate in large scale, wired scenarios, build their routing infrastructure as a set of brokers connected in an acyclic network. The topology of such network is critical for the performance of the system. Depending on the traffic profile, the same topology may provide good performance or be very inefficient. Starting from this consideration, in this paper we first analyze this issue in detail, then we describe a distributed algorithm to address it, by adapting the topology of a content-based publish-subscribe routing network to the application demand
Group velocity mismatch compensation in cw lasers mode-locked by second order nonlinearities
No full textSharp Estimates for the Szegő Projection on the Distinguished Boundary of Model Worm Domains
No full textIn this paper we study the regularity of the Szegő projection on Lebesgue and Sobolev spaces on the distinguished boundary of the unbounded model worm domain DβDβ . We denote by db(Dβ)db(Dβ) the distinguished boundary of DβDβ and define the corresponding Hardy space H2(Dβ)H2(Dβ) . This can be identified with a closed subspace of L2(db(Dβ),dσ)L2(db(Dβ),dσ) , that we denote by H2(db(Dβ))H2(db(Dβ)) , where dσdσ is the naturally induced measure on db(Dβ)db(Dβ) . The orthogonal Hilbert space projection :L2(db(Dβ),dσ)→H2(db(Dβ))P:L2(db(Dβ),dσ)→H2(db(Dβ)) is called the Szegő projection on the distinguished boundary. We prove that P , initially defined on the dense subspace L2∩Lp(db(Dβ),dσ)L2∩Lp(db(Dβ),dσ) extends to a bounded operator :Lp(db(Dβ),dσ)→Lp(db(Dβ),dσ)P:Lp(db(Dβ),dσ)→Lp(db(Dβ),dσ) if and only if 21+νβπνβ=π2β−π,β>π . Furthermore, we also prove that P defines a bounded operator :Ws,2(db(Dβ),dσ)→Ws,2(db(Dβ),dσ)P:Ws,2(db(Dβ),dσ)→Ws,2(db(Dβ),dσ) if and only if 0≤s<νβ20≤s<νβ2 where Ws.2(db(Dβ),dσ)Ws.2(db(Dβ),dσ) denotes the Sobolev space of order s and underlying L2L2 -norm. Finally, we prove a necessary condition for the boundedness of P on Ws,p(db(Dβ),dσ)Ws,p(db(Dβ),dσ) , p∈(1,∞)p∈(1,∞) , the Sobolev space of order s and underlying LpLp -norm
Upconversion-induced fluorescence in multicomponent systems: Steady-state excitation power threshold
Full text linkWe have analyzed the dynamics of the upconversion-induced delayed fluorescence for a model multicomponent organic system, in which high concentrations of triplet states can be sustained in steady-state conditions. At different excitation powers, two regimes have been identified depending on the main deactivation channel for the triplets, namely, the spontaneous decay and the bimolecular annihilation. The excitation power density at which triplet bimolecular annihilation becomes dominant is the threshold (I(th)) to have efficient upconversion generation. The simple equation obtained for I(th) allows us to predict the theoretical efficiency of a generic system on the basis of few parameters of the constituent molecules
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