Singular integrals with rough kernels on product spaces
Singular integrals with rough kernels on product spaces
Suppose that \Omega(x', y')\in L^{1}(S^{n-1}\cross S^{m-1}) is a homogeneous function of degree zero satisfying the mean zero property (1.1), and that h(s, t) is a bounded function on \mathbb{R}\cross \mathbb{R} .The singular integral operator Tf on the product space \mathbb{R}^{n}\cross \mathbb{R}^{m}(n\geq 2, m\geq 2) is defined by \tau f(\xi,\eta)=p.v .\int_{IR^{n}\cross …