Boundedness of singular integral operators of Calderón type
A. Calderón, R. Coifman, A. McIntosh, Y. Meyer, G. David, and others have studied singular integral operators with kernels of type \[ C[h,\Phi]\quad(x,y)=(1/x-y)\quad(h\{\Phi(x)-\Phi(y)/(x-y)\} \] for complex-valued function h and real-valued functions \(\Phi\) [\textit{A. Calderón}, Proc. Natl. Acad. Sci. USA 53, 1092-1099 (1965; Zbl 0151.169), \textit{R. R. Coifman}, \textit{A. McIntosh, and \textit{Y. Meyer}}, Ann. Math., II. Ser. 116, 361-387 (1982; Zbl 0497.42012)]. They found out that C(h,\(\Phi]\) is of type 2 if h is infinitely differentiable and \(\Phi\) ' is essentially bounded. The purpose of this paper is to give a new proof of this theorem. The author will deduce this theorem from Calderón's theorem [loc.cit.] and so called ''good \(\lambda\) inequalities''.
singular integral operators of Calderón type
scientific article; zbMATH DE number 3861752