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This article is cited in 9 scientific papers (total in 9 papers)
On differentiability of functions in $L^p$, $0<p<1$
V. G. Krotov
Abstract:
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 $L^p$, $0<p<1$; an analogous question is considered for boundary values of analytic functions in the Hardy classes $H^p$, $0<p<1$. 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.
Received: 25.02.1981
Citation:
V. G. Krotov, “On differentiability of functions in $L^p$, $0<p<1$”, Mat. Sb. (N.S.), 117(159):1 (1982), 95–113; Math. USSR-Sb., 45:1 (1983), 101–119
Linking options:
https://www.mathnet.ru/eng/sm2184https://doi.org/10.1070/SM1983v045n01ABEH002589 https://www.mathnet.ru/eng/sm/v159/i1/p95
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Abstract page: | 481 | Russian version PDF: | 151 | English version PDF: | 16 | References: | 39 |
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