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Medientyp:
E-Artikel
Titel:
Optimal Lpand Holder Estimates for the Kohn Solution of the ∂̄-Equation on Strongly Pseudoconvex Domains
Beteiligte:
Chang, Der-Chen E.
Erschienen:
American Mathematical Society, 1989
Erschienen in:Transactions of the American Mathematical Society
Sprache:
Englisch
ISSN:
0002-9947
Entstehung:
Anmerkungen:
Beschreibung:
<p>Let Ω be an open, relatively compact subset in C<sup>n+1</sup>, and assume the boundary of Ω, ∂Ω, is smooth and strongly pseudoconvex. Let Op(K) be an integral operator with mixed type homogeneities defined on Ω̄: i.e., K has the form as follows: ∑<sub>k,l≥ 0</sub>E<sub>kH</sub>
<sub>l</sub>, where E<sub>k</sub>is a homogeneous kernel of degree -k in the Euclidean sense and H<sub>l</sub>is homogeneous of degree -l in the Heisenberg sense. In this paper, we study the optimal L<sup>p</sup>and Holder estimates for the kernel K. We also use Lieb-Range's method to construct the integral kernel for the Kohn solution<tex-math>$\overline{\partial^\ast}N$</tex-math>of the Cauchy-Riemann equation on the Siegel upper-half space and then apply our results to<tex-math>$\overline{\partial^\ast}N$</tex-math>. On the other hand, we prove Lieb-Range's kernel gains 1 in "good" directions (hence gains 1/2 in all directions) via Phong-Stein's theory. We also discuss the transferred kernel from the Siegel upper-half space to Ω.</p>