Schatten–von Neumann properties in the Weyl calculus
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- 作者：Ernesto Buzano ; Joachim Toft
- 关键词：Hö ; rmander symbols ; Schatten– ; von Neumann classes ; Embeddings ; Necessary conditions ; Sufficient conditions
- 刊名：Journal of Functional Analysis
- 出版年：2010
- 出版时间：15 December 2010
- 年：2010
- 卷：259
- 期：12
- 页码：3080-3114
- 全文大小：273 K
文摘
Let , for tR, be the pseudo-differential operator and let be the set of Schatten–von Neumann operators of order p[1,∞] on L2. We are especially concerned with the Weyl case (i.e. when t=1/2). We prove that if m and g are appropriate metrics and weight functions respectively, hg is the Planck's function, for some k0 and aS(m,g), then , iff aLp. Consequently, if 0δ<ρ1 and , then is bounded on L2, iff aL∞.