  This paper is devoted to presenting new interior regularity criteria in terms
of one velocity component for weak solutions to the Navier-Stokes equations in
three dimensions. It is shown that the velocity is regular near a point $z$ if
its scaled $L^p_tL^q_x$-norm of some quantities related to the velocity field
is finite and the scaled $L^p_tL^q_x$-norm of one velocity component is
sufficiently small near $z$.
