Singular integral operators with rough kernels on central Morrey spaces with variable exponent

This is the authors' abstract. We don't add key points for this paper.

In this paper we define the -central BMO spaces and the central Morrey spaces with variable exponent. We obtain the boundedness of the singular integral operator T , and its commutator [b, T , ] on central Morrey spaces with variable exponent, where L s (S n-1 ) for s 1 be homogeneous function of degree zero, 0 < n and b be -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 V M O coefficients.