Boundedness of Operators Related to a Degenerate Schrödinger Semigroup

Autor: Beatriz Eleonora Viviani, Eleonor Ofelia Harboure, Oscar Mario Salinas
Rok vydání: 2021
Předmět:
Zdroj: Potential Analysis. 57:401-431
ISSN: 1572-929X
0926-2601
Popis: In this work we search for boundedness results for operators related to the semigroup generated by the degenerate Schrodinger operator ${{\mathscr{L}}} u = -\frac {1}{\omega } \text {div} A\cdot \nabla u +V u$ , where ω is a weight, A is a matrix depending on x and satisfying λω(x)|ξ|2 ≤ A(x)ξ ⋅ ξ ≤Λω(x)|ξ|2 for some positive constants λ, Λ and all x, ξ in $\mathbb {R}^{d}$ , 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, ${{\mathscr{L}}}^{-\alpha /2}$ , the negative powers of ${{\mathscr{L}}}$ , and the mixed operators ${{\mathscr{L}}}^{-\alpha /2}V^{\sigma /2}$ with 0 < σ ≤ α on appropriate functions 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, obtaining also some boundedness properties in this context that we believe are new.
Databáze: OpenAIRE
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