Functional calculus on weighted Sobolev spaces for the Laplacian on the
half-space
Functional calculus on weighted Sobolev spaces for the Laplacian on the
half-space
In this paper, we consider the Laplace operator on the half-space with Dirichlet and Neumann boundary conditions. We prove that this operator admits a bounded $H^\infty$-calculus on Sobolev spaces with power weights measuring the distance to the boundary. These weights do not necessarily belong to the class of Muckenhoupt $A_p$ …