Nikodym sets and maximal functions associated with spheres

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510981" target="_blank" >RIV/00216208:11320/25:10510981 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xjNE_sVJky" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xjNE_sVJky</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RMI/1519" target="_blank" >10.4171/RMI/1519</a>

Result language
angličtina
Original language name
Nikodym sets and maximal functions associated with spheres
Original language description
We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp Lp-estimates for Nikodym maximal functions associated with spheres. As a corollary, any Nikodym set for spheres must have full Hausdorff dimension. In addition, we consider a class of maximal functions which contains the spherical maximal function as a special case. We show that Lp-estimates for these maximal functions can be deduced from local smoothing estimates for the wave equation relative to fractal measures.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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