Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Triebel--Lizorkin spaces
Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Triebel--Lizorkin spaces
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Besov和Triebel--Lizorkin空间中的椭圆边界问题和Boutet de Monvel演算
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
J. Johnsen
中科院分区：
文献类型：
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作者：
J. Johnsen
伪微分边界算子的Boutet de Monvel微积分推广到Besov和triiebel—Lizorkin空间的满尺度（尽管后者具有有限的积分指数）。本文证明的连续性和Fredholm性质扩展了Franke和Grubb先前得到的性质，并且关于满椭圆Green算子的值域补的结果改进了先前已知的结果，甚至对于$1<p<infty$的经典空间也是如此。处理的符号类是统一估计的符号类。给出了0类格林迹算子和奇异算子的一般定义的一些精度。
The Boutet de Monvel calculus of pseudo-differential boundary operators is generalised to the full scales of Besov and Triebel--Lizorkin spaces (though with finite integral exponents for the latter). The continuity and Fredholm properties proved here extend those previously obtained by Franke and Grubb, and the results on range complements of surjectively elliptic Green operators improve the earlier known, even for the classical spaces with $1<p<infty$. The symbol classes treated are the uniformly estimated ones. Some precisions are given for the general definitions of trace and singular Green operators of class 0.