Fundamental solutions and mapping properties of semielliptic operators
G. N. Hile · Mathematische Nachrichten · 2006
Abstract An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces in ℝn . Necessary and sufficient conditions are given for such a mapping to be an isomorphism. Results apply, for example, to elliptic, parabolic, and generalized p ‐parabolic operators. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)