On approximate differentiability of the maximal function
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10053651" target="_blank" >RIV/00216208:11320/10:10053651 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On approximate differentiability of the maximal function
Original language description
We prove that if f is integrable and approximately differentiable a.e., then the Hardy-Littlewood maximal function Mf is also approximately differentiable a.e. Moreover, if we only assume that f is integrable, then any open set of R^n contains a subset of positive measure such that Mf is approximately differentiable on that set. On the other hand we present an example of an integrable function on R such that Mf is not approximately differentiable a.e.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F06%2F0198" target="_blank" >GA201/06/0198: Theory of real functions and descriptive set theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
138
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
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UT code for WoS article
000273614200018
EID of the result in the Scopus database
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