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We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain of dimension . If is a smooth manifold of dimension and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in with the same smooth -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in vanishes or if is polynomially...
Let D be a bounded strictly pseudoconvex domain of with smooth boundary. We consider the weighted mixed-norm spaces of holomorphic functions with norm . We prove that these spaces can be obtained by real interpolation between Bergman-Sobolev spaces and we give results about real and complex interpolation between them. We apply these results to prove that is the intersection of a Besov space with the space of holomorphic functions on D. Further, we obtain several properties of the mixed-norm...
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