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On the continuity of discrete maximal operators in Sobolev spaces
Hannes LuiroJuho Nuutinensubject
Discrete mathematicsSobolev spaceGeneral Mathematicsta111Maximal operatorPartition (number theory)Modulus of continuityCounterexampleSobolev inequalitySobolev spaces for planar domainsMathematicsdescription
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-02-01 | Annales Academiae Scientiarum Fennicae Mathematica |