A singular integral operator along a hypersurface.

摘要

In this paper we show that for a class of h and f the singular integral operator Tfx&ar; =h yW yy nfx-y,xn+1-f ydy , where x&ar;∈Rn+1 and x,y ∈ Rn, is bounded for f ∈ Lp for a range of p. Counter examples are provided for additinal ranges of p. This paper extends the work of Lung-Kee Chen and Henry Lin.[1]