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Boundedness of fractional integral operators on weighted Herz spaces. (Chinese. English summary) Zbl 0981.42011
Based on atomic decomposition theory, the authors obtain, under some conditions, the boundedness of fractional integral operators from the weighted Herz-type spaces \(\dot K^{\alpha,p}_{q_1}(\omega_1, \omega^{q_1}_2)\) (or \(K^{\alpha,p}_{q_1}(\omega_1, \omega^{q_1}_2)\)) into \(\dot K^{\alpha,p}_{q_2}(\omega_1, \omega^{q_2}_2)\) (or \(K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\)) and from the weighted Herz-type Hardy spaces \(H\dot K^{\alpha, p}_{q_1}(\omega_1, \omega^{q_1}_2)\) (or \(HK^{\alpha, p}_{q_1}(\omega_1, \omega^{q_1}_2)\)) into \(\dot K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\) (or \(K^{\alpha, p}_{q_2}(\omega_1, \omega^{q_2}_2)\)), respectively.
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47B38 Linear operators on function spaces (general)
47G10 Integral operators
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems