实单位球上的面积积分算子
Area Integral Operator on the Real Unit Ball

作者: 王东方 :湖南大学数学与计量经济学院; 马柏林 , 沈丹桂 :嘉兴学院数理与信息工程学院;

关键词: 面积积分算子Carleson测度单位球单位球面Area Integral Operator Carleson Measure The Unit Ball The Unit Sphere

摘要:
本文通过Carleson boxes或者Tents的方式定义了实单位球上的Carleson测度,并建立了单位球上非切极大函数、Poisson积分和Carleson测度之间的联系。作为一个应用,我们引入一种中单位球体上非负测度相关的面积积分算子,并用Carleson测度和其他方式刻画了这种使得或从有界的非负测度

Abstract:
In this paper, we introduce Carleson measures on the real unit ball in terms of Carleson boxes or tents, and establish relations among the non-tangential maximal function, Poisson integral and Carleson measures on the real unit ball. As an application, we introduce a certain area integral operator involving a nonnegative measure on the unit ball and characterize the measure in terms of Carleson measure and other forms such that maps from to or from to .

文章引用: 王东方 , 马柏林 , 沈丹桂 (2013) 实单位球上的面积积分算子。 理论数学, 3, 56-67. doi: 10.12677/PM.2013.31010

参考文献

[1] P. Ahern, J. Bruna. Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of . Revista Matemática Iberoameri- cana, 1988, 4(1): 123-153.

[2] W. S. Cohn. Generalized area operator on Hardy spaces. Journal of Mathematical Analysis and Applications, 1997, 216(1): 112-121.

[3] Z. Wu. Area operator on Bergman spaces. Science in China Series A, 2006, 49(7): 987-1008.

[4] M. Gong, Z. Lou and Z. Wu. Area operators from spaces to spaces. Science China Mathematics, 2010, 53(2): 357-366.

[5] J. B. Garnett. Bounded analytic functions. New York: Academic Press, 1982.

[6] E. S. Stein. Harmornic analysis, real variable, orthogonality, and oscillatory integrals. Princeton: Princeton University Press, 1993.

[7] L. Grafakos. Classical and modern Fourier analysis. Beijing: China Machine Press, 2005.

[8] C. A. Nolder. A characterization of certain measures using Quasiconformal mappings. Proceedings of the American Mathematical Society, 1990, 109(2): 349-356.

[9] P. L. Duren. Extension of a theorem of Carleson. Bulletin of the American Mathematical Society, 1969, 75(1): 143-146.

[10] L. Carleson. An interplation problem for bounded analytic functions. American Journal of Mathematics, 1958, 80(4): 921-930.

分享
Top