Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Boundedness of admissible area function on nonisotropic Lipschitz space

Author(s): Jinshou Gao; Houyu Jia
Journal: Proc. Amer. Math. Soc. 133 (2005), 1777-1785.
MSC (2000): Primary 47B38, 32A37, 42B25
Posted: December 20, 2004
MathSciNet review: 2120278
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $B$ be the unit ball in $C^n$, let $S$ be the unit sphere, and let $S_\beta (f)$ be the admissible area function. In this paper, we show that if $f\in Lip_\alpha (S)$, then $S_\beta (f)\in Lip_\alpha (S)$ and there exists a constant $C$ such that $\Vert S_\beta (f)\Vert _{Lip_\alpha}\le C \Vert f\Vert _{Lip_\alpha}$.

References:

1.
W. Rudin, Function Theory in the unit ball of $C^n$, Springer-Verlag, New York, 1980. MR 0601594 (82i:32002)

2.
S. Y. Chang, A generalized area integral estimate and applications, Studia Math. 69 (1980), 109-120. MR 0604343 (82d:42014)

3.
P. Ahern and J. Bruna, Maximal and area integral characterization of Hardy-Sobolev spaces in the unit ball of $C^n$, Rev. Mat. Iber. 4 (1988), 123-153. MR 1009122 (90h:32011)

4.
S. G. Krantz, Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups, J. Func. Anal. 34 (1979) 456-471.MR 0556266 (81j:32020)

5.
H. Kang and H. Koo, Two weight inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball, Nagoya Math. J. 58 (2000), 107-131. MR 1766570 (2002b:32008)

6.
E. M. Stein, Singular Integrals and Differentiability properties of Functions, Princeton Univ. Press, Princeton, 1970. MR 0290095 (44 #7280)

7.
S.G. Krantz and S. Y. Li, Area integral characterizations of functions in Hardy space on domains in $C^n$, Complex Variables Theory Appl. 32 (1997), 373-399. MR 1459599 (98m:32003)

8.
A. Bonami, J. Bruna and S. Grellier, On Hardy, BMO and Lipschitz spaces of invariantly harmonic functions in the unit ball, Proc. Lond. Math. Soc. 77 (1998), 665-696. MR 1643425 (99g:31008)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B38, 32A37, 42B25

Retrieve articles in all Journals with MSC (2000): 47B38, 32A37, 42B25

Additional Information:

Jinshou Gao
Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People's Republic of China
Address at time of publication: Department of Mathematics, Zhejiang University, Hangzhou, 310028, People's Republic of China
Email: gaojinshou@yahoo.com.cn

Houyu Jia
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310028, People's Republic of China
Email: mjhy@zju.edu.cn

DOI: 10.1090/S0002-9939-04-07733-0
PII: S 0002-9939(04)07733-0
Keywords: Unit ball in $C^n$, admissible area function, nonisotropic Lipschitz space
Received by editor(s): September 17, 2003
Received by editor(s) in revised form: February 20, 2004
Posted: December 20, 2004
Additional Notes: The second author was supported in part by the Education Department of Zhejiang Province
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia