ESTIMATES FOR CONE MULTIPLIERS ASSOCIATED WITH HOMOGENEOUS FUNCTIONS

Abstract

Let rho is an element of C(infinity)(R(n) \ {0}) be homogeneous of degree one. We show that the convolution operator (T(delta)f) over cap(xi', xi(n+1)) = (1 - rho(xi')/vertical bar xi(n+1)vertical bar)(delta) (f) over cap(xi', xi(n+1)), (xi', xi(n+1)) is an element of R(n) x R(1) is bounded from Hardy spaces H(P)(R(n+1)) to L(P)(R(n+1)) for delta > n(1/p - 1/2) - 1/2, 0 < p < 1.