Abstract :
We study the singular integral operator
fx,t (y ) = f (x − ty ),
defined on all test functions f, where b is a bounded function, α 0, Ω is suitable
distribution on the unit sphere Sn−1 satisfying some cancellation conditions. We prove
certain boundedness properties of TΩ,α on the Triebel–Lizorkin spaces and on the Besov
spaces. We also use our results to study the Littlewood–Paley functions. These results
improve and extend some well-known results.
2002 Elsevier Science (USA). All rights reserved.
