Mathematische Nachrichten ( IF 0.910 ) Pub Date : 2020-11-20 , DOI: 10.1002/mana.201900052
Ryutaro Arai; Eiichi Nakai; Yoshihiro Sawano

The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space $H Φ ( R n )$ to another Orlicz–Hardy space $H Ψ ( R n )$, where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator $I α$ from $H p ( R n )$ to $H q ( R n )$ for $α , p , q ∈ ( 0 , ∞ )$ and $− n / p + α = − n / q$, which was proved by Stein and Weiss in 1960.

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