Certain Operators with Rough Singular Kernels

http://dx.doi.org/10.4153/CJM-2003-021-4
Canad. J. Math. 55(2003), 504-532

  Published:2003-06-01
 Printed: Jun 2003

We study the singular integral operator $$ T_{\Omega,\alpha}f(x) = \pv \int_{R^n} b(|y|) \Omega(y') |y|^{-n-\alpha} f(x-y)\,dy, $$ defined on all test functions $f$,where $b$ is a bounded function, $\alpha\geq 0$, $\Omega(y')$ is an integrable function on the unit sphere $S^{n-1}$ satisfying certain cancellation conditions. We prove that, for $1

MSC Classifications:

42B20, 42B25, 42B15 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.) Maximal functions, Littlewood-Paley theory Multipliers 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory 42B15 - Multipliers