An L (q) (L (p) )-Theory for Parabolic Pseudo-Differential Equations: Caldern-Zygmund Approach

In this paper we present a Caldern-Zygmund approach for a large class of parabolic equations with pseudo-differential operators of arbitrary order . It is assumed that (t) is merely measurable with respect to the time variable. The unique solvability of the equation are obtained for any lambda > 0 and lambda > 0 and p,q is an element of(1,infinity)