caa a22 4500 445836709 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0781-7 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0781-7 Alexandre William Laboratoire Paul Painlevé U.M.R. CNRS 8524, U.F.R. de Mathématiques, Université Lille 1, 59655, Villeneuve d'Ascq Cedex, France aut A Berndtsson-Andersson operator solving $${\overline{\partial}}$$ -equation with W α -estimates on convex domains of finite type [Elektronische Daten] [William Alexandre] The Carleson measures were first introduced by Carleson in order to solve the corona problem for the disc in $${\mathbb{C}}$$ . The notion of Carleson measure can be generalized to any homogeneous space and were also used in the context of the corona problem in $${\mathbb{C}^n}$$ for example by Varopoulos, Amar and Andersson and Carlsson. One of the steps to solve the H p corona problem in a pseudoconvex domain is to solve the $${\overline\partial}$$ equation for a formμ satisfying a Carleson condition and get norm estimates of the solution in term of the Carleson norm ofμ. The main goal of this paper is to consider this question in the case of convex domains of finite type and to get estimates linked to the multitype of the domain. Springer-Verlag, 2010 Carleson measure nationallicence Berndtsson-Andersson integral operator nationallicence Bergman metric nationallicence Bergman kernel nationallicence Convex domain nationallicence Finite type nationallicence $${\overline\partial}$$ -Equation nationallicence Corona problem nationallicence Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 1155-1180 0025-5874 269:3-4<1155 2011 269 209 https://doi.org/10.1007/s00209-010-0781-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0781-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Alexandre William Laboratoire Paul Painlevé U.M.R. CNRS 8524, U.F.R. de Mathématiques, Université Lille 1, 59655, Villeneuve d'Ascq Cedex, France aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 1155-1180 0025-5874 269:3-4<1155 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer