Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain \({\Omega}\), with boundary data in the Besov space \({B_{s}^{p,p} (\partial\Omega).}\) The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p 1 was treated.