Singular integral operators of near-product-type on the Heisenberg group
- 作者：Andrea Fraser
- 关键词：Heisenberg group ; Product-type singular integral operators ; Product group ; Calderó ; n– ; Zygmund singular integral operators ; Marcinkiewicz multipliers ; Transference ; Reverse transference ; Normalized bump function
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2007
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：15 March 2007
- 卷：327
- 期：2
- 页码：1225-1243
- 文件大小：233 K
摘要
In this paper we establish Lp-boundedness (1<p<∞) for a class of singular convolution operators on the Heisenberg group whose kernels satisfy regularity and cancellation conditions adapted to the implicit (n+1)-parameter structure. The polyradial kernels of this type arose in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35–58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353–376] as the convolution kernels of (n+1)-fold Marcinkiewicz-type spectral multipliers of the n-partial sub-Laplacians and the central derivative on the Heisenberg group. Thus they are in a natural way analogous to product-type Calderón–Zygmund convolution kernels on . Here, as in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35–58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353–376], we extend to the (n+1)-parameter setting the methods and results of Müller, Ricci, and Stein in [D. Müller, F. Ricci, E.M. Stein, Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups I, Invent. Math. 119 (1995) 199–233] for the two-parameter setting and multipliers of the sub-Laplacian and the central derivative.