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.

scholarly journals Weighted Multilinear Hardy Operators on Herz Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shuli Gong ◽  
Zunwei Fu ◽  
Bolin Ma
Keyword(s):  
Weight Function ◽  
Sufficient Condition ◽  
Herz Spaces ◽  
Type Spaces ◽  
Hardy Operators

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces.

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