Generalized Non-Autonomous Kato Classes and Nonlinear Bessel Potentials

In this dissertation, we study the scale of function spaces M_p(Rⁿ) introduced by Zamboni. For these spaces, we get a characterization in terms of nonlinear Bessel potentials. This result is based on a known characterization of the Kato class K_n,s of order s in terms of Bessel potentials. We also introduce and study new function classes P^p_n,T([0,T] x Rⁿ) and A^p_n,T([0,T] x Rⁿ) these classes generalize the classes P_n,T([0,T] x Rⁿ) and A_n,T([0,T] x Rⁿ) introduced by Gulisashvili.