ID  84173 
Author 
Ito, Yoshifumi
Professor Emeritus, The University of Tokushima
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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^pfunctions and L_loc^pfunctions in the sense of L^pconvergence and L_loc^pconvergence 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 L2functions and L_loc^2functions，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
