Commutators of weighted Hardy operators on Herz-type spaces

2011 ◽  
Vol 101 (3) ◽  
pp. 267-273 ◽  
Author(s):  
Canqin Tang ◽  
Feien Xue ◽  
Yu Zhou
2021 ◽  
Vol 13 (2) ◽  
pp. 522-533
Author(s):  
C. Aykol ◽  
Z.O. Azizova ◽  
J.J. Hasanov

In this paper, we find sufficient conditions on general Young functions $(\Phi, \Psi)$ and the functions $(\varphi_1,\varphi_2)$ ensuring that the weighted Hardy operators $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ from $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ to $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.


2019 ◽  
Vol 249 (2) ◽  
pp. 143-162
Author(s):  
David E. Edmunds ◽  
Alexander Meskhi

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shuli Gong ◽  
Zunwei Fu ◽  
Bolin Ma

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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