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

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概要

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• 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 donot need the theory of distributions except the case p = 1.Thereby，I give the new characterization of Soboley spaces and givethe 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.

著者

• Ito Yoshifumi

  The University Of Tokushima

関連論文

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