This paper outlines an approach for studying operators on stratified spaces \(M \in \mathfrak {M}_k\) with regular singularities of higher order k. Smoothness corresponds to \(k=0.\) Manifolds with smooth boundaries belong to the category \(\mathfrak {M}_1.\) The case \(k=1\) generally indicates conical or edge singularities. Boutet de Monvel’s algebra of boundary value problems (BVPs) with the transmission property at the boundary may be interpreted as a special singular operator calculus for \(k=1.\) Also, BVPs A with violated transmission properties belong to edge calculus and are controlled by pairs \(\{\sigma _j(A)\}_{ j=0,1},\) consisting of interior and boundary symbols. Singularities of \(M \in \mathfrak {M}_k\) for higher order k give rise to a sequence of strata \(s(M)=\{s_j(M) \}_{ j=0,\ldots ,k},\) where \(s_j(M)\in \mathfrak {M}_0.\) Operators A in corresponding algebras of operators (corner-degenerate in stretched variables) are determined by a hierarchy of symbols \(\sigma (A)=\{\sigma _j(A)\}_{ j=0,\ldots ,k},\) modulo lower order terms. Those express ellipticity and parametrices \(A^{(-1)}\) in weighted corner Sobolev spaces, containing sequences of real weights \(\gamma _j.\) Components \(\sigma _j(A)\) for \(j>0,\) depending on variables and covariables in \(T^*(s_j(M))\setminus 0,\) act as operator families on infinite straight cones with compact singular links in \(\mathfrak {M}_{j-1},\) and \(\sigma _0(A)\) is the standard principal symbol on \(T^*(s_0(M))\setminus 0.\)

本文概述了一种研究分层空间\(M \in \mathfrak {M}_k\)上的算子的方法，该空间具有高阶k 的规则奇点。平滑度对应于\(k=0.\)边界平滑的流形属于类别\(\mathfrak {M}_1.\)情况\(k=1\)一般表示圆锥形或边缘奇点。Boutet de Monvel 的边界值问题 (BVP) 代数具有边界处的传输特性，可以解释为\(k=1.\)的特殊奇异算子演算。此外，具有违反传输特性的BVP A属于边微积分，并且是由对控制\(\{\sigma _j(A)\}_{ j=0,1},\)由内部符号和边界符号组成。\(M \in \mathfrak {M}_k\)对于高阶k 的奇点产生了一系列地层\(s(M)=\{s_j(M) \}_{ j=0,\ldots ， k},\)其中\(s_j(M)\in \mathfrak {M}_0.\)对应算子代数中的算子A（拉伸变量中的角退化）由符号的层次结构\(\sigma ( A)=\{\sigma _j(A)\}_{ j=0,\ldots ,k},\)模低阶项。那些明确椭圆率和parametrices \（A ^ {（ - 1）} \）在加权角Sobolev空间，实际权重的含有序列\（\伽马_j \。）组件\（\西格玛_j（A）\）为\(j>0,\)取决于\(T^*(s_j(M))\setminus 0,\) 中的变量和协变量作为运算符族在无限直锥体上，在\(\mathfrak {M }_{j-1},\)和\(\sigma _0(A)\)是\(T^*(s_0(M))\setminus 0.\)上的标准主符号