Geodesic
On differentiability of functions in $L^p$, $0$
Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 101-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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V. G. Krotov. On differentiability of functions in $L^p$, $0

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