Pseudo-annular decomposition and approximate rate of Calderón–Zygmund operators on Heisenberg group

2015 ◽  
Vol 13 (01) ◽  
pp. 1550001
Author(s):  
Pengtao Li ◽  
Heping Liu ◽  
Lizhong Peng ◽  
Qixiang Yang
Keyword(s):  
Heisenberg Group ◽  
Zygmund Operator ◽  
Approximate Rate

Let T be a Calderón–Zygmund operator on Heisenberg group ℍd. In this paper, by wavelets, we introduce a class of pseudo-annular operators {TR}R≥1 to decompose T. By controlling the bandwidth of TR, we could obtain the approximate rate of T from L2(ℍd) to L2(ℍd) at an ideal rate.

scholarly journals Construction of Frames on the Heisenberg Groups

2020 ◽  
Vol 8 (1) ◽  
pp. 382-395
Author(s):  
Der-Chen Chang ◽  
Yongsheng Han ◽  
Xinfeng Wu
Keyword(s):  
Fourier Transform ◽  
Heisenberg Group ◽  
Operator Theory ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Identity Operator ◽  
Heisenberg Groups ◽  
Zygmund Operator ◽  
The Fourier Transform

Abstract In this paper, we present a construction of frames on the Heisenberg group without using the Fourier transform. Our methods are based on the Calderón-Zygmund operator theory and Coifman’s decomposition of the identity operator on the Heisenberg group. These methods are expected to be used in further studies of several complex variables.

Weighted estimates for commutators of Hausdorff operators on the Heisenberg group

2020 ◽  
pp. 39-62
Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

The horofunction boundary of the Heisenberg group

2009 ◽  
Vol 242 (2) ◽  
pp. 299-310 ◽  
Author(s):  
Tom Klein ◽  
Andrew Nicas
Keyword(s):  
Heisenberg Group

scholarly journals Weighted CBMO estimates for commutators of matrix Hausdorff operator on the Heisenberg group

2020 ◽  
Vol 18 (1) ◽  
pp. 496-511
Author(s):  
Amna Ajaib ◽  
Amjad Hussain
Keyword(s):  
Heisenberg Group ◽  
Herz Spaces ◽  
Hausdorff Operator ◽  
Hausdorff Operators

Abstract In this article, we study the commutators of Hausdorff operators and establish their boundedness on the weighted Herz spaces in the setting of the Heisenberg group.

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