论文标题
schr {Ö} dinger操作员在能量空间中的界限
Boundedness of Schr{ö}dinger operator in energy space
论文作者
论文摘要
On a complete weighted Riemannian manifold $(M^n,g,μ)$ satisfying the doubling condition and the Poincar{é} inequalities, we characterize the class of function $V$ such that the Schr{ö}dinger operator $Δ-V$ maps the homogeneous Sobolev space $W_o^{1,2} (M)$ to its dual space.在欧几里得空间上，这个结果归功于马兹亚和韦尔比茨基。为了证明我们的结果，我们研究了霍奇投影仪的加权$ l^2 $结合。
On a complete weighted Riemannian manifold $(M^n,g,μ)$ satisfying the doubling condition and the Poincar{é} inequalities, we characterize the class of function $V$ such that the Schr{ö}dinger operator $Δ-V$ 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.
