Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces
| dc.creator | Maas, Jan | |
| dc.creator | van Neerven, Jan | |
| dc.date | 2008-04-09 | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:20Z | |
| dc.date.available | 2026-07-07T10:17:20Z | |
| dc.description | Let (E,H,mu) be an abstract Wiener space and let D_V := VD, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space G. Given a bounded operator B on G, coercive on the closure of the range of V, we consider the realisation of the operator D_V* B D_V in L^p(E,mu) for 1<p<\infty. Our main result states that the following assertions are equivalent: (1) dom((sqrt(D_V* B D_V)) = dom(D_V) and Meyer's inequalities hold for D_V* B D_V; (2) D_V D_V* B admits a bounded H-infinity calculus on the closure of the range of D_V; (3) dom(sqrt(V*BV)) = dom(V) and Meyer's inequalities hold for V*BV; (4) VV*B admits a bounded H-infinity calculus on the closure of the range of V. Moreover, if these conditions are satisfied, then dom(L) = dom(D_V^2) \cap dom(D_A). The equivalence of (1)-(4) is a non-symmetric generalisation of the classical Meyer inequalities (which correspond to the case G=H, V=I, B=I). A one-sided version of the main result, giving L^p-boundedness of the associated Riesz transforms in terms of a square function estimate, is also obtained. As an application let -A generate an analytic C_0-contraction semigroup on a Hilbert space H and let -L be the L^p-realisation of the generator of its second quantisation. Our results imply that two-sided bounds for the Riesz transform of L are equivalent with the Kato square root property for A. | |
| dc.description | 54 pages, submitted for publication. Minor corrections | |
| dc.identifier | https://arxiv.org/abs/0804.1432 | |
| dc.identifier | http://arxiv.org/abs/0804.1432 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173820 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 60H07 (Primary); 35J15, 35K90, 35R15, 47A60, 47B44, 47D05, 47F05, 60H30, 60G15 (Secondary) | |
| dc.title | Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces | |
| dc.type | text |