ID 110916
著者
キーワード
Lp-calculus
Lp-function
Lp-differentiability
Lp-derivative
partial Lp-derivative
Lploc-function
Lploc-differentiability
Lploc-derivative
partial Lploc-derivative
資料タイプ
紀要論文
抄録
In this paper, we define the derivative or the partial derivative of a Lp-function in the sense of Lp-convergence. We also define the derivative and the partial derivative of a Lploc-function in the sense of Lploc-convergence. Then we study their fundamental properties. Here assume that 1 ≤ p ≤ ∞ holds.
We say that the branch of analysis on the bases of the concepts of Lp-convergence and Lploc-convergence is the Lp-calculus.
As the results, we have the following conclusions for the differential calculus of classical functions.
Assume that 1 ≤ p ≤ ∞. Then we have the inclusion relations Lp ⊂ Lploc ⊂ L1loc. In the Lp-calculus, the derivative or the partial derivatives of a Lp-function are the derivative or the partial derivatives of the function calculated in the sense of L1loc-topology which are the Lp-functions for each p, (1 < p ≤ ∞) respectively.
For Lploc-functions, we have the similar results.
Especially, the L1-derivative or the partial L1-derivatives of a L1-function are the L1loc-derivative or the partial L1loc-derivatives in the above sense, respectively. But the inverse facts are not necessarily true.
掲載誌名
Journal of Mathematics
ISSN
13467387
cat書誌ID
AA11595324
50
開始ページ
91
終了ページ
111
並び順
91
発行日
2016
フルテキストファイル
言語
eng
著者版フラグ
出版社版
部局
理工学系