SINGULAR INTEGRAL OPERATORS WITH ROUGH KERNELS ON CENTRAL MORREY SPACES WITH VARIABLE EXPONENT

In this paper we define the lambda-central BMO spaces and the central Morrey spaces with variable exponent. We obtain the boundedness of the singular integral operator T-Omega,T-alpha and its commutator [b, T-Omega,T-alpha] on central Morrey spaces with variable exponent, where Omega is an element of L-s (Sn-1) for s >= 1 be homogeneous function of degree zero, 0 <= alpha < n and b be lambda-central BMO functions. As applications, we consider the regularity in the central Morrey spaces with variable exponent of strong solutions to nondivergence elliptic equations with VMO coefficients.