Zeros Sets Of H^p Functions In Lineally Convex Domains Of Finite Type In C^n
In this note we extend N. Th. Varopoulos result on zero sets of H p functions of strictly pseudo-convex domains in C n to lineally convex domains of finite type.
math.CV↗
arXiv subjects
Y Dupain
Publications and source records attributed to Y Dupain.
Weighted and boundary l p estimates for solutions of the $\partial$ -equation on lineally convex domains of finite type and applications
We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($Ω$,$δ$ $γ$), $δ$ being the distance to the boundary, with two different types of hypothesis on the form f : first, if the data f belongs to L p $Ω$,$δ$ $γ$ $Ω$ , $γ$ > --1, we have a mixed gain on the index p and the exponent $γ$; secondly we obtain a similar estimate when the data f satisfies an apropriate anisotropic L p estimate with weight $δ$ $γ$+1 $Ω$. Moreover we extend those results to $γ$ = --1 and obtain L p ($\partial$ $Ω$) and BMO($\partial$ $Ω$) estimates. These results allow us to extend the L p ($Ω$,$δ$ $γ$)-regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.
math.CV↗
Weighted estimates for solutions of the $\partial$ -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 $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p (Ω,$δ$ $γ$), $δ$ being the distance to the boundary, with gain on the index p and the exponent $γ$. These estimates allow us to extend the L p (Ω,$δ$ $γ$) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.
math.CV↗