Geodesic
On differentiability of functions in $L^p$, $0$
Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 101-119

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In this paper the author studies the connection between smoothness, expressed in terms of the integral modulus of continuity, and the existence of a derivative, understood in some sense, for functions in $L^p$, $0$; an analogous question is considered for boundary values of analytic functions in the Hardy classes $H^p$, $0$. A connection is established between the derivatives of an analytic function in $H^p$ and the derivatives of its boundary value; both global and pointwise derivatives are considered. Bibliography: 25 titles. 
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     author = {V. G. Krotov},
     title = {On differentiability of functions in $L^p$, $0<p<1$},
     journal = {Sbornik. Mathematics},
     pages = {101--119},
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     volume = {45},
     number = {1},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_1_a6/}
}
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V. G. Krotov. On differentiability of functions in $L^p$, $0