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| Home > Articles > Published articles > Lp bounds for Riesz transforms and square roots associated to second order elliptic operators |
| Date: | 2003 |
| Abstract: | We consider the Riesz transforms ∇L-1/2, where L≡- divA(x)∇, and A is an accretive, n × n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the square root problem of T. Kato. |
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| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Subject: | Riesz transforms ; Square roots of divergence form elliptic operators |
| Published in: | Publicacions matemàtiques, V. 47 N. 2 (2003) , p. 497-515, ISSN 2014-4350 |
