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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
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