Differential Calculus for L^p-functions and L_loc^p-functions Revisited

• Ito, Yoshifumi

抄録

I studied the concepts of differentiability，derivatives and partial derivatives as the fundamental concepts of differential calculus in Ito [4]，[5] . ln this paper, we study the fundamental properties of derivatives and partal derivatives of classical functions such as L^p-functions and L_loc^p-functions in the sense of L^p-convergence and L_loc^p-convergence respectively. Here we assume that p is a real number such that 1≤p<∞ holds. ln the calculation of such derivatives and partial derivatives，we do not need the theory of distributions except the case p = 1. Thereby，I give the new characterization of Soboley spaces and give the new meaning of Stone's Theorem. Especially，in the cases of L2-functions and L_loc^2-functions，these results have the essential role in the study of Schrödinger equations.

収録刊行物

• Journal of mathematics, the University of Tokushima

  Journal of mathematics, the University of Tokushima 45 49-66, 2011

  徳島大学

詳細情報

• CRID: 1050001337734599168
• NII論文ID: 110008729467
• NII書誌ID: AA11595324
• ISSN: 13467387
• Web Site: http://repo.lib.tokushima-u.ac.jp/84173
• 本文言語コード: en
• 資料種別: departmental bulletin paper
• データソース種別:
  • IRDB
  • CiNii Articles