Fractional integrals on weighted Hardy spaces. (English) Zbl 1031.42014
Summary: In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces \(H^p_w(\mathbb{R}^n)\), we give the weighted boundedness of the homogeneous fractional integral operator \(T_{\Omega,\alpha}\) from \(H^p_{w^p}(\mathbb{R}^n)\) to \(L^q_{w^q}(\mathbb{R}^n)\), and from \(H^p_{w^p}(\mathbb{R}^n)\) to \(H^q_{w^q}(\mathbb{R}^n)\).
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B30 | \(H^p\)-spaces |
| 47G10 | Integral operators |
Keywords:
\(A_p\) weights; fractional integrals; \(L^r\)-Dini condition; weighted Hardy spaces; atomic decompositionReferences:
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