TY - JOUR
T1 - Singular Integrals Associated with Zygmund Dilations
AU - Han, Yongsheng
AU - Li, Ji
AU - Lin, Chin Cheng
AU - Tan, Chaoqiang
N1 - Publisher Copyright:
© 2018, The Author(s).
PY - 2019/7/15
Y1 - 2019/7/15
N2 - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on R3 associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on Lp, 1 < p< ∞.
AB - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on R3 associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on Lp, 1 < p< ∞.
KW - Multi-parameter singular integral operators
KW - Zygmund dilations
KW - Zygmund type cancellation
UR - http://www.scopus.com/inward/record.url?scp=85052661907&partnerID=8YFLogxK
U2 - 10.1007/s12220-018-0081-8
DO - 10.1007/s12220-018-0081-8
M3 - 期刊論文
AN - SCOPUS:85052661907
SN - 1050-6926
VL - 29
SP - 2410
EP - 2455
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -