直近一年間の累計
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ID 84173
著者
資料タイプ
紀要論文
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.
掲載誌名
Journal of mathematics, the University of Tokushima
ISSN
13467387
cat書誌ID
AA11595324
45
開始ページ
49
終了ページ
66
並び順
49
発行日
2011
フルテキストファイル
言語
eng
部局
理工学系