TY - JOUR
T1 - Boundedness of Parabolic Singular Integrals and Marcinkiewicz Integrals on Triebel-Lizorkin Spaces
AU - Y. M. Niu & S. P. Tao
JO - Analysis in Theory and Applications
VL - 1
SP - 59
EP - 75
PY - 2011
DA - 2011/01
SN - 27
DO - http://doi.org/10.1007/s10496-011-0059-x
UR - https://global-sci.org/intro/article_detail/ata/4580.html
KW - parabolic singular integral, Triebel-Lizorkin space, Marcinkiewica integral,
rough kernel.
AB - <p style="text-align: justify;">In this paper, we obtain the boundedness of the parabolic singular integral operator $T$ with kernel in $L(\log L)^{1/ \gamma} (S^{n−1})$ on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals $\mu_{\Omega,q}(f)$ from $\|f\|_{\dot{F}_{p}^{0,q}(\mathbf{R}^n)}$ into $L^p(\mathbf{R}^n)$.</p>