ترغب بنشر مسار تعليمي؟ اضغط هنا

Regularity of the Bergman projection on forms and plurisubharmonicity conditions

213   0   0.0 ( 0 )
 نشر من قبل Anne-Katrin Herbig
 تاريخ النشر 2005
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Let D be a smoothly bounded domain in a complex vector space of dimension n. Suppose that D has a smooth defining function, such that the sum of any q eigenvalues of its complex Hessian are non-negative on the closure of D. We show that this implies global regularity of the Bergman projection on (0,j)-forms for j larger or equal to q-1.



قيم البحث

اقرأ أيضاً

We obtain sharp ranges of $L^p$-boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating $L^p$-bounde dness on a domain and its quotient by a finite group. The range of $p$ for which the Bergman projection is $L^p$-bounded on our class of Reinhardt domains is found to shrink as the complexity of the domain increases.
This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the kernel, and to L^p mapping properties of the kernel.
162 - L. D. Edholm , J. D. McNeal 2015
A class of pseudoconvex domains in $mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the fatness of domains. This range of $p$ is shown to be sharp.
We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman-Constantin and obtain the following estimate for the weighted norm of $P$: [|P|_{L^2(Omega,W)}leq C(ma thcal B_2(W))^{{2}}.] Here $mathcal B_2(W)$ is the Bekolle-Bonami constant for the matrix weight $W$ and $C$ is a constant that is independent of the weight $W$ but depends upon the dimension and the domain.
It is shown that even a weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $mathcal C^1$ boundary: the product of the Bergman kernel by the volume of the indicatrix of the Azukawa metric is not bounded below. Th is is obtained by finding a direction along which the Sibony metric tends to infinity as the base point tends to the boundary. The analogous statement fails for a Lipschitz boundary. For a general $mathcal C^1$ boundary, we give estimates for the Sibony metric in terms of some directional distance functions. For bounded pseudoconvex domains, the Blocki-Zwonek Suita-type theorem implies growth to infinity of the Bergman kernel; the fact that the Bergman kernel grows as the square of the reciprocal of the distance to the boundary, proved by S. Fu in the $mathcal C^2$ case, is extended to bounded pseudoconvex domains with Lipschitz boundaries.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا