SOBOLEV-TYPE EMBEDDING THEOREMS FOR HARMONIC AND HOLOMORPHIC SOBOLEV SPACES

Title & Authors

SOBOLEV-TYPE EMBEDDING THEOREMS FOR HARMONIC AND HOLOMORPHIC SOBOLEV SPACES
Cho, Hong-Rae; Kwon, Ern-Gun;

Abstract

In this paper we consider Sobolev-type embedding theorems for harmonic and holomorphic Sobolev spaces on a bounded domain with ${$C^2$}$ boundary.

Keywords

Sobolev-type embedding;harmonic Sobolev space;holomorphic Sobolev space;

Language

English

Cited by

The Mixed Norm Spaces of Polyharmonic Functions, Potential Analysis, 2007, 27, 2, 167

References

F. Beatrous, $L^p$ estimates for extensions of holomorphic functions, Michigan Math. J. 32 (1985), 361–380.

F. Beatrous, Estimates for derivatives of holomorphic functions in pseudoconvex domains, Math. Z. 191 (1986), 91-116.

F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 256 (1989), 1-57.

H. R. Cho and E. G. Kwon, Growth rate of the functions in Bergman type spaces, submitted

W. Rudin, Function theory in the unit ball of $C^n$, Spinger-Verlag, New York, 1980

E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970