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Vector-valued fractional integral on Herz-type Hardy spaces. (English) Zbl 0949.42015
Summary: In this paper, it is proved that the fractional integral operators with vector-valued kernels are bounded from the Herz-type Hardy spaces $$HK_p$$, into vector-valued Herz spaces, $$K_{E,q}$$. Applications are given to fractional-order maximal function operators, approximate identities and fractional integrals.
##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 42B30 $$H^p$$-spaces 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35 Function spaces arising in harmonic analysis