Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces (Analysis in Theory and Applications, 2018)
In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ γ} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $μ_{Ω,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(R^n)}$ into $L^p(R^n)$.
Keywords: parabolic singular integral; Triebel-Lizorkin space; Marcinkiewica integral; rough kernel.