Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 253-271
MSC: Primary 42B20; Secondary 42B25.
DOI: 10.4064/cm133-2-12
Abstract
Some weighted sharp maximal function inequalities for the Toeplitz type operator $T_b=\sum_{k=1}^mT^{k,1}M_bT^{k,2}$ are established, where $T^{k,1}$ are a fixed singular integral operator with non-smooth kernel or $\pm I$ (the identity operator), $T^{k,2}$ are linear operators defined on the space of locally integrable functions, $k=1,\ldots ,m$, and $M_b(f)=bf$. The weighted boundedness of $T_b$ on Morrey spaces is obtained by using sharp maximal function inequalities.
