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Potential Analysis

, Volume 34, Issue 3, pp 261–282 | Cite as

On Complementary Spaces of the Lizorkin Spaces

  • Takahide Kurokawa
Article
  • 43 Downloads

Abstract

Let \({\cal S}(R^n)\) be the Schwartz space on R n . 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 \({\cal S}(R^n)\).

Keywords

Lizorkin spaces Complementary spaces 

Mathematics Subject Classification (2010)

46E10 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of Science, Department of Mathematics and Computer ScienceKagoshima UniversityKagoshimaJapan

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