On maximal operators along surfaces

In this paper, we establish the boundedness of the following maximal operat or Mf(x, x(n)) = sup(r>0) {1/r(n-1) integral(\y\less than or equal to r) \f(x- y, x(n) - Gamma(y)\dy}(x, y is an element of Rn-1, x(n) is an element of R) on L-P(R-n) for all p > 1, n greater than or equal to 2, where Gamma(y) = Gamma(\y\) is a real, measurable, and radial function defined on Rn-1.