Local approximations by solutions hypoelliptic equations, and removable singularities
This paper deals with several properties of the solutions of quasihomogeneous hypoelliptic linear differential operators with constant coefficients. The author introduces the functional spaces \(U_p\subset L_p\), the anisotropic Campanato classes \(C_p\), the anisotrophic Morrey class \(W_p\). In Theorems 1-3, relations of the type \(U_p\subset C_p\), \(1\leq p< \infty\), \(U_p= W_p\) are shown. Under some conditions it is announced that for homogeneous elliptic operators of order \(m>1\), \(1\leq p\leq \infty\) the class \(U_p\) coincides with the Hölder-Zygmund class \(\Lambda^s\). In Theorems 6, 7, removability of the singularities of solutions to the equation \(P(D)u=0\) are established. No proofs or sketches of the proofs are given.
scientific article; zbMATH DE number 1557739