1,215 research outputs found
Weighted estimates for solutions of the -equation for lineally convex domains of finite type and applications to weighted bergman projections
In this paper we obtain sharp weighted estimates for solutions of the
-equation in a lineally convex domains of finite type. Precisely we
obtain estimates in spaces of the form L p ({\Omega}, ),
being the distance to the boundary, with gain on the index p and the
exponent . These estimates allow us to extend the L p
({\Omega}, ) and lipschitz regularity results for weighted
Bergman projection obtained in [CDM14b] for convex domains to more general
weights
Estimates for some Weighted Bergman Projections
In this paper we investigate the regularity properties of weighted Bergman
projections for smoothly bounded pseudo-convex domains of finite type in
. The main result is obtained for weights equal to a non
negative rational power of the absolute value of a special defining function
of the domain: we prove (weighted) Sobolev- and Lipchitz
estimates for domains in (or, more generally, for domains
having a Levi form of rank and for "decoupled" domains) and for
convex domains. In particular, for these defining functions, we generalize
results obtained by A. Bonami & S. Grellier and D. C. Chang & B. Q. Li. We also
obtain a general (weighted) Sobolev- estimate.Comment: Final version. To appear in Complex Variables and Elliptic Equation
Extremal Bases, Geometrically Separated Domains and Applications
We introduce the notion of extremal basis of tangent vector fields at a
boundary point of finite type of a pseudo-convex domain in . Then
we define the class of geometrically separated domains at a boundary point, and
give a description of their complex geometry. Examples of such domains are
given, for instance, by locally lineally convex domains, domains with locally
diagonalizable Levi form, and domains for which the Levi form have comparable
eigenvalues at a point. Moreover we show that these domains are localizable.
Then we define the notion of "adapted pluri-subharmonic function" to these
domains, and we give sufficient conditions for his existence. Then we show that
all the sharp estimates for the Bergman ans Szeg\"o projections are valid in
this case. Finally we apply these results to the examples to get global and
local sharp estimates, improving, for examlple, a result of Fefferman, Kohn and
Machedon on the Szeg\"o projection.Comment: 37 pages. Final version to appear in St. Petersburg Math.
On the zero sets of bounded holomorphic functions in the bidisc
In this work we prove in a constructive way a theorem of Rudin which says that if is an analytic subset of the bidisc (with multiplicities) which does not intersect a neighbourhood of the distinguished boundary, then is the zero set (with multiplicities) of a bounded holomorphic function. This approach allows us to generalize this theorem and also some results obtained by P.S.Chee
On the zero sets of bounded holomorphic functions in the bidisc
In this work we prove in a constructive way a theorem of Rudin which says
that if is an analytic subset of the bidisc (with
multiplicities) which does not intersect a neighbourhood of the
distinguished boundary, then is the zero set (with multiplicities) of
a bounded holomorphic function. This approach allows us to generalize this
theorem and also some results obtained by P.S. Chee
Un système de transmission hyperfréquence d'images et de données numériques pour le télécontrôle d'engins mobiles en milieux confinés
National audienceLe telecontrôIe d'engins mobiles en milieux encombres ou confines comme les chantiers miniers ou de genie civile pose le difficile probleme de la transmission hertzienne a haut debit, alors que l'usage de cables specialises s'avere hasardeux en raison des risques de rupture ou d'arrachement
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