Zhang, Chaonan; Zhou, Jiang; Cao, Yonghui The boundedness of generalized fractional integral operators on the weighted homogeneous Morrey-Herz spaces. (Chinese. English summary) Zbl 1363.42027 J. Math., Wuhan Univ. 36, No. 1, 199-206 (2016). Summary: In this article, we study the boundedness of the generalized fractional integral operators on the weighted homogeneous Morrey-Herz spaces. By the methods of studying ring decomposition of functions and truncated operators, we get that the generalized fractional integral operator \(L^{-\beta/2}(f)\) is bounded from \(M\dot{K}_{p, q_1}^{\alpha, \lambda} (\omega_1, \omega_2^{q_1})\) space to \(M\dot{K}_{p, q_2}^{\alpha, \lambda} (\omega_1, \omega_2^{q_2})\) space. Thus, we extend the results of the boundedness of the fractional integral operators on the weighted homogeneous Morrey-Herz spaces to generalized fractional integral operators. MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35 Function spaces arising in harmonic analysis Keywords:generalized fractional integral operators; the weighted homogeneous Morrey-Herz spaces; \(A_p\) weight PDFBibTeX XMLCite \textit{C. Zhang} et al., J. Math., Wuhan Univ. 36, No. 1, 199--206 (2016; Zbl 1363.42027)