Sobolev Spaces Associated to the Harmonic Oscillator

[摘要] We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= -𝛥 + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.

[学科分类] 数学（综合）

[关键词] Hermite operator;potential spaces;Riesz transforms.