ID 84173
Author
Content Type
Departmental Bulletin Paper
Description
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.
Journal Title
Journal of mathematics, the University of Tokushima
ISSN
13467387
NCID
AA11595324
Volume
45
Start Page
49
End Page
66
Sort Key
49
Published Date
2011
FullText File
language
eng
departments
Science and Technology