Singular integral operators along surfaces of revolution

Let h, γ , and φ be radial functions on Rn and let Ω ∈ H1(Sn−1). Under certain natural conditions on γ and φ, we obtain Lp boundedness for the singular integral operators Tα,βf (x,xn+1) = p.v. Rn h |y| Ω(y )ei|y|−β |y|−n−αf x −y, xn+1 − γ |y| dy and Tf (x,xn+1) = p.v. Rn h |y| Ω(y )|y|−nf x − φ |y| y ,xn+1 − γ |y| dy. We also proved the Lp boundedness for the maximal operator associated with Tf .  2002 Elsevier Science (USA). All rights reserved