Sobolev spaces, Lebesgue points and maximal functions

Sobolev spaces, Lebesgue points and maximal functions

In this note, we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such maximal operators.

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Veröffentlicht in:Journal of fixed point theory and applications 2013-03, Vol.13 (1), p.259-269
Hauptverfasser: Hajłasz, Piotr, Liu, Zhuomin
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Zusammenfassung:In this note, we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such maximal operators.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-013-0111-x