## Nagoya Mathematical Journal

### {$L\sp p$}-extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary

Kenzō Adachi

#### Abstract

Let $D$ be a bounded strictly pseudoconvex domain in ${\mathbb C}^{n}$ (with not necessarily smooth boundary) and let $X$ be a submanifold in a neighborhood of $\overline{D}$. Then any $L^{p}$ $(1 \leq p < \infty)$ holomorphic function in $X \cap D$ can be extended to an $L^{p}$ holomorphic function in $D$.

#### Article information

Source
Nagoya Math. J., Volume 172 (2003), 103-110.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631957

Mathematical Reviews number (MathSciNet)
MR2019521

Zentralblatt MATH identifier
1067.32009

#### Citation

Adachi, Kenzō. {$L\sp p$}-extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary. Nagoya Math. J. 172 (2003), 103--110. https://projecteuclid.org/euclid.nmj/1114631957

#### References

• F. Beatrous, 361–380, $L^p$ estimates for extensions of holomorphic functions (1985, 32, Michigan Math. J. ).
• H. R. Cho, 89–91, A counterexample to the $L^p$ extension of holomorphic functions from subvarieties to pseudoconvex domains (1998, 35, Complex Variables ).
• A. Cumenge, 59–97, Extension dan des classes de Hardy de fonctions holomorphes et estimations de type “mesures de Carleson” pour l'equation $\partial$ (1983, 33, Ann. Inst. Fourier ).
• G. M. Henkin, 536–563, Continuation of bounded holomorphic functions from submanifolds in general position in a strictly pseudoconvex domain (1972, 6, Math. USSR Izv. ).
• G. M. Henkin and J. Leiterer, Theory of functions on complex manifolds, Birkhäuser (1984).
• T. Ohsawa and K. Takegoshi, 197–204, On the extension of $L^2$ holomorphic functions (1987, 195, Math. Z. ).
• G. Schmalz, 409–430, Solution of the $\bar\partial$-equation with uniform estimates on strictly $q$-convex domains with non-smooth boundary (1989, 202, Math. Z. ).