Bernstein inequality in Lα norms
The classical Bernstein inequality estimates the derivative of a polynomial at a fixed point with the supremum norm and a factor depending on the point only. Recently, this classical inequality was generalized to arbitrary compact subsets on the real line. That generalization is sharp and naturally...
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| További közreműködők: | |
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2013
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| Sorozat: | Acta scientiarum mathematicarum
79 No. 1-2 |
| Kulcsszavak: | Matematika, Bernstein-egyenlőtlenség |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/30868 |
| Tartalmi kivonat: | The classical Bernstein inequality estimates the derivative of a polynomial at a fixed point with the supremum norm and a factor depending on the point only. Recently, this classical inequality was generalized to arbitrary compact subsets on the real line. That generalization is sharp and naturally introduces potential theoretical quantities. It also gives a hint how a sharp La Bernstein inequality should look like. In this paper we prove this conjectured La Bernstein type inequality and we also prove its sharpness. |
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| Terjedelem/Fizikai jellemzők: | 129-174 |
| ISSN: | 0001-6969 |