A remark on the boundedness of Calderon-Zygmund operators in non-homogeneous spaces

作者：Fu Xiao Li; Hu Guo En; Yang Da Chun^*

来源：Acta Mathematica Sinica-English Series, 2007, 23(3): 449-456.

DOI：10.1007/s10114-005-0723-1

• Calderon-Zygmund operator
• Hardy space
• L1(,infinity)(mu)
• non-doubling measure

Let mu be a Radon measure on Rd which may be non-doubling. The only condition satisfied by mu is that mu(B(x, r)) <= Cr (n) for all x is an element of R-d, r > 0 and some fixed 0 < n <= d. In this paper, the authors prove that the boundedness from H (1)(mu) into L (1,infinity)(mu) of a singular integral operator T with Calderon-Zygmund kernel of Hormander type implies its L (2)(mu)-boundedness.

• 出版日期2007-3
• 单位北京师范大学; 中国人民解放军信息工程大学