Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space.
Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ
We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.
Tangential Cauchy-Riemann equations on quadratic manifolds
We study the tangential Cauchy-Riemann equations for -forms on quadratic manifolds. We discuss solvability for data in the Schwartz class and describe the range of the tangential Cauchy-Riemann operator in terms of the signatures of the scalar components of the Levi form.
On some spaces of holomorphic functions of exponential growth on a half-plane
In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...
Eigenvalues of the Hodge Laplacian on the Heisenberg group.
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