The goal of this paper is to characterize the local sharp estimate $$(I_{\rho } f)^{\#}(x) \le C \, M_{\rho } f(x)$$ and by using this inequality to get necessary and sufficient conditions on the triple functions $$(\varphi , \rho , \omega )$$ which satisfy the equivalence of norms of the generalized fractional integral operator $$I_{\rho }$$ and the generalized fractional maximal operator $$M_{\rho }$$ on the generalized weighted Morrey spaces $${\mathcal {M}}_{p,\varphi }({\mathbb {R}}^{n},\omega )$$ and generalized weighted central Morrey spaces $$\dot{{\mathcal {M}}}_{p,\varphi }({{\mathbb {R}}}^n,\omega )$$, when $$\omega \in A_{\infty }$$-Muckenhoupt class.

中文翻译：

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广义分数阶积分算子和广义分数极大算子在广义加权莫雷空间上的范数等价

本文的目标是刻画局部尖锐估计 $$(I_{\rho } f)^{\#}(x) \le C \, M_{\rho } f(x)$$ 并通过使用这个不等式得到满足广义分数积分算子 $$I_{\rho }$$ 和广义分数的范数等价的三元函数 $$(\varphi , \rho , \omega )$$广义加权莫雷空间上的极大算子 $$M_{\rho }$$ $${\mathcal {M}}_{p,\varphi }({\mathbb {R}}^{n},\omega )$ $ 和广义加权中心莫雷空间 $$\dot{{\mathcal {M}}}_{p,\varphi }({{\mathbb {R}}}^n,\omega )$$, 当 $$\ omega \in A_{\infty }$$-Muckenhoupt 类。