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- W2114500020 abstract "It is shown that para-multiplication applies to a certain product π(u, v) defined for appropriate u and v in 𝒴'(IRn). Boundedness of π(.,.) is investigated for the anisotropic Besov and Triebel-Lizorkin spaces - i.e., for BM,s/p,q and FM,s/p,q with s ∈ R and p and q in [0, ∞] (though p < ∞ in the F-case) - with a treatment of the generic as well as of various borderline cases. For max (so,s,) > 0 the spaces BM,so/p,qo ⊕ BM,so/p,qo and BM,so/p,qo ⊕ BM,so/p,qo to which π(.,.) applies arc determined. For generic Bso/po,qo ⊕ Bs1/p1,q1 the receiving Fsp,q spaces are characterized. It is proved that π(f, g) = f · g holds for functions f and g when f · g ∈L1,loc, roughly speaking. In addition, π(f, u) = fu when f ∈ 𝒪M and u ∈𝒴' . Moreover, for an arbitrary open set Ω⊆ IRn, a product πΩ(., .) is defined by lifting to IRn. Boundedness of n on R′ is shown to carry over to πΩ is general." @default.
- W2114500020 created "2016-06-24" @default.
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- W2114500020 date "1995-01-01" @default.
- W2114500020 modified "2023-10-16" @default.
- W2114500020 title "Pointwise Multiplication of Besov and Triebel-Lizorkin Spaces" @default.
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- W2114500020 doi "https://doi.org/10.1002/mana.19951750107" @default.
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