Schatten-von Neumann Properties in the Weyl Calculus, and Calculus of Metrics on Symplectic Vector Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Schatten-von Neumann Properties in the Weyl Calculus, and Calculus of Metrics on Symplectic Vector Spaces

Authors:

Joachim Toft

Affiliation:

1. Department of Mathematics and Systems Engineering, V?xj? University, V?xj?, Sweden

Abstract:

Let s ^wp be the set of all a ∈ ? such that a ^w(x, D) is Schatten p-operator on L ². Then we prove the following:

$S(m,g)subseteq s_p^wLet s ^wp be the set of all a ∈ ℓ such that a ^w(x, D) is Schatten p-operator on L ². Then we prove the following:

•	iff . Furthermore, when $h_g^{N/2}min L^p$ . Consequently, $S^r_{rho, delta}cap L^infty subseteq s^w_infty$ when ;
•	if , then is symplectically invariantly defined. Moreover, if and $gle g^{sigma}$ is slowly varying (and σ-temperate), then the same is true for G;
•	a generalization of sharp G?rding's inequality.

Mathematics Subject Classifications (2000) Primary: 35S05, 47B10, 47L15 Secondary: 32F45, 16W80

Keywords:

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