L^p-differentiability of W^(l,P)(R^n)(1<P<+∞) functions

FROM ref. [1] it is known that every L^P(R^n) (1≤p【+ ∞) function, is L^P-continuous, 1.e. Further result about L^P-continuity has been obtained in ref. [2], §Ⅰ. 4, which is the following Proposition. Proposition. Let f∈L^P(R^n , 1【 p≤+∞. Then (?)_jf∈L^p, 1≤j≤n, if and only if ‖f(x+h)-f(x)‖L^p=O(|h|),where (?)_jf is the jth partial derivative for f in the sense of S’, i. e.