Symbolic calculus and the transposes of bilinear pseudodifferential operators
Symbolic calculus and the transposes of bilinear pseudodifferential operators
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DOI：
10.1081/pde-120021190
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发表时间：
2003-01-01
影响因子：
1.9
通讯作者：
Torres, RH
中科院分区：
文献类型：
--
作者：
Bényi, A;Torres, RH
建立了一类双线性伪微分算子转置的符号演算。利用微积分得到了勒贝格空间积的有界性结果。一个更大的伪微分算子类，不允许微积分也被考虑。这类算子是所谓奇异类线性伪微分算子的双线性模拟，在Lebesgue空间的积上不能产生有界算子。然而，我们证明了算子在Sobolev空间的正平滑积上是有界的，推广了函数积的莱布尼茨规则估计。
A symbolic calculus for the transposes of a class of bilinear pseudodifferential operators is developed. The calculus is used to obtain boundedness results on products of Lebesgue spaces. A larger class of pseudodifferential operators that does not admit a calculus is also considered. Such a class is the bilinear analog of the so-called exotic class of linear pseudodifferential operators and fail to produce bounded operators on products of Lebesgue spaces. Nevertheless, the operators are shown to be bounded on products of Sobolev spaces with positive smoothness, generalizing the Leibniz rule estimates for products of functions.