6533b83afe1ef96bd12a71ce

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On the continuous and discontinuous maximal operators

Hannes Luiro

subject

0301 basic medicineClass (set theory)Applied Mathematicsta111010102 general mathematicsoperatorsSingular integralcontinuity01 natural sciencesInfimum and supremumCombinatorics03 medical and health sciences030104 developmental biologySobolev spacesBounded functionjatkuvuusMaximal operator0101 mathematicsmaximal operatorAnalysisoperaattorit (matematiikka)Mathematics

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Abstract In the first part of this paper we study the regularity properties of a wide class of maximal operators. These results are used to show that the spherical maximal operator is continuous W 1 , p ( R n ) ↦ W 1 , p ( R n ) , when p > n n − 1 . Other given applications include fractional maximal operators and maximal singular integrals. On the other hand, we show that the restricted Hardy–Littlewood maximal operator M λ , where the supremum is taken over the cubes with radii greater than λ > 0 , is bounded from L p ( R n ) to W 1 , p ( R n ) but discontinuous.

yearjournalcountryeditionlanguage
2018-07-01Nonlinear Analysis
https://doi.org/10.1016/j.na.2017.12.016