Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch −δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator.
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机译：令M为n维的紧流形，P = P（h）是M上的半经典伪微分算子，而u = u（h）是L 2 归一化函数族，使得P（h）在L 2 （M）中，u（h）为O（h），为h↓0。令H⊂M是M的紧凑子流形。在上一篇文章中，第二作者证明了u的L p 范数p≥2的估计值限于H，假设u是半经典局部的，并且在关于P的主符号的某些自然结构假设下。这些估计的形式为Ch -δ（n，k，p），其中k = dim H（除了a k = n-2，p = 2的情况下的对数散度。当H是一个超曲面时，即k = n-1，我们有δ（n，n-1，2）= 1/4，当M是一个圆形的n球体并且H是一个赤道时，这很锐利。
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