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| The boundedness of singular integral operators is one of the core contents in modern harmonic analysis research. The fractional integral operators are a kind of important singular integral operators based on partial differential equations in harmonic analysis, and its boundedness in various function spaces is a very significant subject. In this paper, using the properties of the weight functions $A_{(p,q)}$, and the pointwise estimates of $T_{\Omega,\alpha}$ and $[b,T_{\Omega,\alpha}],$ we investigated the boundedness of the fractional integral operators with rough kernels $T_{\Omega,\alpha}$ and the high-order commutators $T_{\Omega,\alpha}^{m,b}$ generated by $T_{\Omega,\alpha}$ and BMO functions in vanishing generalized weighted Morrey spaces. |
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| Keywords:fractional integral operator; commutator; BMO function; vanishing generalized weighted Morrey space |
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