Nondivergence parabolic equations in weighted variable exponent spaces

We prove the global Calderón-Zygmund estimates for second order parabolic equations in nondivergence form in weighted variable exponent Lebesgue spaces. We assume that the associated variable exponent is log-Hölder continuous, the weight is of a certain Muckenhoupt class with respect to the variable exponent, the coefficients of the equation are the functions of small bonded mean oscillation, and the underlying domain is a C 1 , 1 C^{1,1} -domain.