Boundedness of Operators Related to a Degenerate Schrödinger Semigro

E. HARBOURE, O. SALINAS Y B. VIVIANI

POTENTIAL ANALYSIS

SPRINGER

Lugar: Berlin; Año: 2021

0926-2601

In this work we search for boundedness results for operators related to the semigroup generated by the degenerate Schrôdinger operatorLu = − 1/ω div A · ∇u + V u, where ω is a weight, A is a matrix dependingon x and satisfying λ ω(x)|ξ|^2 ≤ A(x)ξ · ξ ≤ Λ ω(x)|ξ|^2for some positive constants λ, Λ and all x, ξ in R^d, assuming further suitable properties on the weight ω and on the non-negative potential V . In particular, we analyze the behaviour of T∗, the maximal semigroup operator, L^−α/2, the negative powers of L, and the mixed operators L^−α/2 V^σ/2 with 0 < σ ≤ α on appropriatefunctions spaces measuring size and regularity. As in the non degenerate case,i.e. ω ≡ 1, we achieve these results by first studying the case V = 0, obtainingalso some boundedness properties in this context that we believe are new.