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The boundedness of generalized fractional integral operators on the weighted homogeneous Morrey-Herz spaces. (Chinese. English summary) Zbl 1363.42027

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
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