Mesure de Mahler et calcul de constantes universelles pour les polynomes de N variables.
In this paper we will prove a Mittag-Leffler type theorem for -closed -forms in by addressing the question of constructing such differential forms with prescribed periods in certain domains.
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...
Besov spaces of holomorphic functions in tubes over cones have been recently defined by Békollé et al. In this paper we show that Besov p-seminorms are invariant under conformal transformations of the domain when n/r is an integer, at least in the range 2-r/n < p ≤ ∞.
It is proved that the Fréchet algebra has exactly three closed subalgebras which contain nonconstant functions and which are invariant, in the sense that whenever and is a biholomorphic map of the open unit ball of onto . One of these consists of the holomorphic functions in , the second consists of those whose complex conjugates are holomorphic, and the third is .
Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces where the Monge-Ampère measure has compact support for the associated exhaustion...
We present a multidimensional analogue of an inequality by van der Corput-Visser concerning the coefficients of a real trigonometric polynomial. As an application, we obtain an improved estimate from below of the Bohr radius for the hypercone 𝓓₁ⁿ = {z ∈ ℂⁿ: |z₁|+. .. +|zₙ| < 1} when 3 ≤ n ≤ 10.