In this paper, we consider the boundedness on Triebel-Lizorkin spaces for the $d$-dimensional Calderón commutator defined by $T_{\Omega,a}f(x)={\rm p.\,v.}\int_{\mathbb{R}^d}\frac{\Omega(x-y)}{|x-y|^{d+1}}\big(a(x)-a(y)\big)f(y){\rm d}y,$ where $\Omega$ is homogeneous of degree zero, integrable on $S^{d-1}$ and has a vanishing moment of order one, and $a$ is a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$. We prove that if $1<p,\,q<\infty$ and $\Omega\in L(\log L)^{2\tilde{q}}(S^{d-1})$ with $\tilde{q}=\max\{1/q,\,1/q'\}$, then $T_{\Omega,a}$ is bounded on Triebel-Lizorkin spaces $\dot{F}_{p}^{0,q}(\mathbb{R}^d)$.
Guoen HU
,
Jie LIU
. BOUNDEDNESS OF THE CALDERÓN COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES∗[J]. Acta mathematica scientia, Series B, 2023
, 43(4)
: 1618
-1632
.
DOI: 10.1007/s10473-023-0411-1
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