In this paper we study spaces of holomorphic functions on the Siegel upper halfspace U and prove Paley-Wiener type theorems for such spaces. The boundary of U can be identified with the Heisenberg group Hn. Using the group Fourier transform on Hn, Ogden-Vagi [OV79] proved a Paley-Wiener theorem for the Hardy space H 2 (U).We consider a scale of Hilbert spaces on U that includes the Hardy space, the weighted Bergman spaces, the weighted Dirichlet spaces, and in particular the Drury-Arveson space, and the Dirichlet space D. For each of these spaces, we prove a Paley-Wiener theorem, some structure theorems, and provide some applications. In particular we prove that the norm of the Dirichlet space modulo constantsḊ is the unique Hilbert space norm that is invariant under the action of the group of automorphisms of U.

Recently, the publish-subscribe communication model has attracted the attention of developers as a viable alternative to traditional communication schemas, like request/reply, for the flexibility it brings to the architecture of distributed applications, by allowing components to be easily added or removed at run-time. At the same time, first experiences in building complex distributed applications using such model point out how it is often hard to live without a request/reply facility.We started from this consideration to introduce replies into the publish-subscribe model in a way that could minimize the impact on the positive characteristics of the model. In this paper we describe the resulting model and present four protocols to implement it, comparing them through the analysis of the results we gathered in running a large testbed on the PlanetLab network.

We study the fractional Laplacian and the homogeneous Sobolev spaces on R d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way we also prove some properties of the fractional Laplacian.

In 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 D β .We denote by d b (D β ) the distinguished boundary of D β and define the corresponding Hardy space H 2 (D β ). This can be identified with a closed subspace ofThe orthogonal Hilbert space projection P :is called the Szegő projection on the distinguished boundary.We prove that P, initially defined on the dense subspace L2β−π , β > π. Furthermore, we also prove that P defines a bounded operator P :denotes the Sobolev space of order s and underlying L 2 -norm.Finally, we prove a necessary condition for the boundedness of P on W s,p (d b (D β ), dσ), p ∈ (1, ∞), the Sobolev space of order s and underlying L p -norm.2010 Mathematics Subject Classification. 32A25, 32A36, 30H20.

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