GlobalL2estimates for a class of Fourier integral operators with symbols in Besov spaces
GlobalL2estimates for a class of Fourier integral operators with symbols in Besov spaces
复制标题
Besov 空间中带符号的一类傅立叶积分算子的 GlobalL2 估计
DOI：
10.1070/rm2003v058n05abeh000671
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发表时间：
2003
影响因子：
0.9
通讯作者：
M. Sugimoto
中科院分区：
文献类型：
--
作者：
M. V. Ruzhanskii;M. Sugimoto
其中a（x, ξ）是符号，φ(y, ξ)是光滑的非退化的一阶正齐次相函数：对于所有τ > 0, φ(y, τξ) = τφ(y, ξ)。注意，通常傅里叶积分算子在x， y， ξ上局部都是(1)的形式。然而，在全局平滑问题中出现的算子在x∈R中具有(1)的整体形式，φ(y, ξ) = ψ(ξ)∙y，其中ψ(ξ)满足| det∇ψ(ξ)|≥C0 >对于所有ξ∈R，我们对它们的全局L性质感兴趣，这由以下定理回答。局部L属性更广为人知，他们的调查是[5]。现在我们将陈述相函数的假设。我们假设存在一个常数C0，使得
where a(x, ξ) is the symbol and φ(y, ξ) is a smooth non-degenerate positively homogeneous of degree one phase function: φ(y, τξ) = τφ(y, ξ) for all τ > 0. Note that in general a Fourier integral operator allways assumes the form (1) locally in x, y, ξ. However, operators arising in the global smoothing problems assume the form (1) globally in x ∈ R with φ(y, ξ) = ψ(ξ) ∙ y, where ψ(ξ) satisfies | det∇ψ(ξ)| ≥ C0 > 0 for all ξ ∈ R. One is interested in their global L properties and this is answered by the following theorems. Local L properties are better known and their survey is in [5]. Now we will state our assumptions for the phase function. We assume that there exists a constant C0 such that