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Dergiler / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 5

Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions

DongYan YU
HuiPing ZHOU
HuiXia MO
Sayfa
851–861
Yayın Tarihi
2022-11-05
DOI
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When DgAi\in \dot{L}bi(0

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Amaç & Hipotez:Let l \in N and \vec{A}=(A1,\dots,Al) and \vec{f}=(f1,\dots,fl) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1,\dots,fl\in Lc\infty(Rn).
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Temel Bulgular & Veri:Let x\notin\capi=1lSupp fi.
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Sonuç & Katkı:When DgAi\in \dot{L}bi(0
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Multilinear fractional integral · commutator · Triebel--Lizorkin space

Özet

Let l \in N and \vec{A}=(A1,\dots,Al) and \vec{f}=(f1,\dots,fl) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1,\dots,fl\in Lc\infty(Rn). Let x\notin\capi=1lSupp fi. The generalized higher commutator generated by the multilinear fractional integral is then given by Ia,m\vec{A}(\vec{f})(x) =\dint(Rn)m \frac{\prod\limitsi=1lRmi+1(Ai;x,yi)fi(yi)}{|(x-y1,\dots ,x-ym)|ln+(m1+m2+\dots+ml)-a} dy1\dots dyl. When DgAi\in \dot{L}bi(0

Abstract

Let l \in N and \vec{A}=(A1,\dots,Al) and \vec{f}=(f1,\dots,fl) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1,\dots,fl\in Lc\infty(Rn). Let x\notin\capi=1lSupp fi. The generalized higher commutator generated by the multilinear fractional integral is then given by Ia,m\vec{A}(\vec{f})(x) =\dint(Rn)m \frac{\prod\limitsi=1lRmi+1(Ai;x,yi)fi(yi)}{|(x-y1,\dots ,x-ym)|ln+(m1+m2+\dots+ml)-a} dy1\dots dyl. When DgAi\in \dot{L}bi(0

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Bu Makaleye Atıf Yap

YU, D., ZHOU, H., MO, H. (2022). Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 5, 851–861. https://ajindex.com/articles/608285

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