On Complementary Spaces of the Lizorkin Spaces

Abstract

Let \({\cal S}(R^n)\) be the Schwartz space on Rn. For a subspace \(V\subset {\cal S}(R^n)\), if a subspace \(W \subset {\cal S}(R^n)\) satisfies the condition that \({\cal S}(R^n)\) is a direct sum of V and W, then W is called a complementary space of V in \({\cal S}(R^n)\). In this article we give complementary spaces of two kinds of the Lizorkin spaces in \({\cal S}(R^n)\).