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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.9 P.1148~1154

http://doi.org/10.1631/jzus.2004.1148


The characterization of weighted local hardy spaces on domains and its application


Author(s):  WANG Heng-geng, YANG Xiao-ming

Affiliation(s):  Department of Mathematics, South-China Normal University, Guangzhou 510631, China; more

Corresponding email(s):   yxm1208@163.net

Key Words:  Weighted local hardy space, Atomic characterization, Lipschitz domain


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WANG Heng-geng, YANG Xiao-ming. The characterization of weighted local hardy spaces on domains and its application[J]. Journal of Zhejiang University Science A, 2004, 5(9): 1148~1154.

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Abstract: 
In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on lipschitz domains. Also, we give their application for the harmonic function defined in bounded lipschitz domains.

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Reference

[1] Chang, D.C., Krantz, S.G., Stein, E.M., 1993. Hp theory on a smooth domain in RN and elliptic boundary value problems. J. Funct. Anal., 114:286.

[2] Lee, M.Y., Lin, C.C., 2002. The molecular characterization of weighted Hardy spaces. J. Funct. Anal., 188:442.

[3] Miyachi, A., 1987. Maximal, functions for distributions onopen sets, Hitotsubashi. J. Arts Sci, 28:45.

[4] Miyachi, A., 1990. HP spaces over open subsets of Rn. Studia Math., 905:205.

[5] Semmes, S., 1994. A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller. C.P.D.E., 19(1&2):277.

[6] Stein, E.M., 1979. Singular Intergrals and Differentiablity Properties of Functions. Princeton University Press, Princeton, New Jersey, p.167-171.

[7] Stein, E.M., 1993. Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Univ. Press, Princeton, New Jersey, p.87-138.

[8] Stromberg, J.O., Torchinsky, A., 1989. Weighted Hardy spaces. Lecture Notes in Mathematics, 1381:111-121.

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