Weighted Hardy operators in local generalized Orlicz-Morrey spaces
Keyword(s):
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 $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.
2021 ◽
Vol 24
(6)
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pp. 1643-1669
Keyword(s):
2010 ◽
Vol 5
(3)
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pp. 531-539
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2012 ◽
Vol 2012
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pp. 1-19
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2013 ◽
Vol 21
(2)
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pp. 111-130