Interpolación en espacios de Bergman-Sobolev.
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Let , and be such that , and let be some admissible functions such that and are equivalent. We first prove that, via the interpolation method, the interpolation of two generalized grand Morrey spaces on a quasi-metric measure space is the generalized grand Morrey space . Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces.
We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can be stated as follows:Let (Ω, A, μ) be any measure space....
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...