Functional composition in B_p,k spaces and applications - Jornet, David; Oliaro, Alessandro (Mathematica Scandinavica, 2006)
Let f(x,z), xR^N, zC^M, be a smooth function in the sense that its Fourier transform has a good behaviour. We study the composition f(x,u(x)), where u is in a generalized Hörmander B_p,k space in the sense of Björck [1]. As a consequence we obtain results of local solvability and hypoellipticity of semilinear equations of the type P(D)u+f(x,Q_1(D)u,…,Q_M(D)u)=g, with gB_p,k, and fully nonlinear elliptic equations.