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

Authors

HUIXIA MO
DONGYAN YU
HUIPING ZHOU

Abstract

Let l \in N and \vec{A}=(A_1,\dots,A_l) and \vec{f}=(f_1,\dots,f_l) be 2 finite collections of functions, where every function A_i has derivatives of order m_i and f_1,\dots,f_l\in L_c^{\infty}(R^n). Let x\notin\cap_{i=1}^lSupp f_i. The generalized higher commutator generated by the multilinear fractional integral is then given by I_{\alpha,m}^{\vec{A}}(\vec{f})(x) =\dint_{(R^n)^m} \frac{\prod\limits_{i=1}^lR_{m_i+1}(A_i;x,y_i)f_{i}(y_i)}{ (x-y_1,\dots ,x-y_m) ^{ln+(m_1+m_2+\dots+m_l)-\alpha}} dy_1\dots dy_l. When D^{\gamma}A_i\in \dot{\Lambda}_{\beta_i}(0

DOI

10.3906/mat-1209-48

Keywords

Multilinear fractional integral, commutator, Triebel--Lizorkin space, Lipschitz function space

First Page

851

Last Page

861

Recommended Citation

MO, HUIXIA; YU, DONGYAN; and ZHOU, HUIPING (2014) "Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions," Turkish Journal of Mathematics: Vol. 38: No. 5, Article 6. https://doi.org/10.3906/mat-1209-48
Available at: https://journals.tubitak.gov.tr/math/vol38/iss5/6