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The higher order commutators of the fractional integrals on Hardy spaces. (English) Zbl 1075.42005
Summary: In this paper we investigate the boundedness on Hardy spaces for the higher order commutator \(T^\tau_{b,m}\) generated by the BMO function \(b\) and a fractional integral type operator \(T^\tau\), and establish the boundedness theorems for \(T^\tau_{b,m}\) from \(H^{p_1,q_1,s}_{b,m}\) to \(L^{p_2}\) and to \(H^{p_2}\) \((0 < p_1\leq 1)\), and from \(H\dot K^{\alpha,p_{1,s}}_{q_1,b,m}\) to \(\dot K^{\alpha,p_2}_{q_2}\) and to \(H\dot K^{\alpha,p_2}_{q_2}\), respectively, for certain ranges of \(\alpha\), \(p_1,q_1,p_2,q_2\) and \(s\).
MSC:
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B30 \(H^p\)-spaces
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