Open AccessFunctional composition in $B_{p,k}$ spaces and applications
Author(s) -
David Jornet,
Alessandro Oliaro
Publication year - 2006
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-15008
Subject(s) - mathematics , composition (language) , space (punctuation) , type (biology) , fourier transform , function (biology) , function space , nonlinear system , combinatorics , pure mathematics , mathematical analysis , physics , linguistics , quantum mechanics , ecology , philosophy , evolutionary biology , biology
Let $f(x,z)$, $x\in\mathsf{R}^N$, $z\in \mathsf{C}^M$, 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 $P(D)u+f(x,Q_1(D)u,\ldots,Q_M(D)u)=g$, with $g\in B_{p,k}$, and fully nonlinear elliptic equations.