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Mat. Zametki, 2004, Volume 76, Issue 5, Pages 762–775 (Mi mz146)  

This article is cited in 2 scientific papers (total in 2 papers)

On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases

G. G. Oniani


Abstract: It is proved that if a convex density-like differential basis $B$ is centered and invariant with respect to translations and homotheties, then the integral means of a nonnegative integrable function with respect to $B$ can boundedly diverge only on a set of measure zero (this generalizes a theorem of Guzmán and Menarguez); it is established that both translation and homothety invariances are necessary.

DOI: https://doi.org/10.4213/mzm146

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English version:
Mathematical Notes, 2004, 76:5, 711–722

Bibliographic databases:

UDC: 517.51
Received: 20.01.2003

Citation: G. G. Oniani, “On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases”, Mat. Zametki, 76:5 (2004), 762–775; Math. Notes, 76:5 (2004), 711–722

Citation in format AMSBIB
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\paper On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases
\jour Mat. Zametki
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\pages 762--775
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\pages 711--722
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Oniani, “Note on Besicovitch's Theorem on the Possible Values of Upper and Lower Derivatives”, Math. Notes, 93:2 (2013), 282–287  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Oniani G., “On the Differentiation of Integrals With Respect to Translation Invariant Convex Density Bases”, Fundam. Math., 246:2 (2019), 205–216  crossref  isi
  • Математические заметки Mathematical Notes
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