BOUNDEDNESS OF SCHRÖDINGER OPERATOR IN ENERGY SPACE

Gilles Carron (1) , Maël Lansade (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 I2M - Institut de Mathématiques de Marseille

On a complete weighted Riemannian manifold $(M^n,g,\mu)$ satisfying the doubling condition and the Poincaré inequalities, we characterize the class of function $V$ such that the Schrödinger operator $\Delta-V$ maps the homogeneous Sobolev space $W_o^{1,2} (M)$ to its dual space. On Euclidean space, this result is due to Maz'ya and Verbitsky. In the proof of our result, we investigate the weighted $L^2$-boundedness of the Hodge projector.

Mots clés: Schrödinger operator, Green kernel, Hodge projector

Domaines: Géométrie différentielle [math.DG]; Théorie spectrale [math.SP]

Gilles Carron, Maël Lansade. BOUNDEDNESS OF SCHRÖDINGER OPERATOR IN ENERGY SPACE. 2022. ⟨hal-03895228⟩