Boundedness for Multilinear Commutators of theta-type Calderón-Zygmund Operator on Herz-Hardy Spaces

2012 ◽  
Author(s):  
Rulong Xie ◽  
Hailian Wang
Keyword(s):  
Hardy Spaces ◽  
Zygmund Operator ◽  
Multilinear Commutators

scholarly journals Endpoint Estimates for Fractional Hardy Operators and Their Commutators on Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jiang Zhou ◽  
Dinghuai Wang
Keyword(s):  
Hardy Spaces ◽  
Herz Spaces ◽  
Multilinear Commutators ◽  
Hardy Operators

(Hpℝn,Lqℝn)bounds of fractional Hardy operators are obtained. Moreover, the estimates for commutators of fractional Hardy operators on Hardy spaces are worked out. It is also proved that the commutators of fractional Hardy operators are mapped from the Herz-type Hardy spaces into the Herz spaces. The estimates for multilinear commutators of fractional Hardy operators are also discussed.

scholarly journals The boundedness of multilinear commutators on locally compact Vilenkin groups

2006 ◽  
Vol 4 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Canqin Tang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Vilenkin Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multilinear Commutators

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces onG. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications

2019 ◽  
Vol 31 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Yan Lin ◽  
Guozhen Lu ◽  
Shanzhen Lu
Keyword(s):  
Maximal Function ◽  
Sharp Maximal Function ◽  
Pointwise Estimates ◽  
Lebesgue Spaces ◽  
Zygmund Operator ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Size Condition ◽  
Multilinear Commutators ◽  
The Mean

Abstract In this paper, we aim to establish the sharp maximal pointwise estimates for the multilinear commutators generated by multilinear strongly singular Calderón–Zygmund operators and BMO functions or Lipschitz functions, respectively. As applications, the boundedness of these multilinear commutators on product of weighted Lebesgue spaces are obtained. It is interesting to note that there is no size condition assumption for the kernel of the multilinear strongly singular Calderón–Zygmund operator. Due to the stronger singularity for the kernel of the multilinear strongly singular Calderón–Zygmund operator, we need to be more careful in estimating the mean oscillation over the small balls to get the sharp maximal function estimates.

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