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Abstract
Let X be a metric space with a doubling measure satisfying μ(B)≳rBn for any ball B with any radius rB> 0. Let L be a non negative selfadjoint operator on L2(X). We assume that e-tL satisfies a Gaussian upper bound and that the flow eitL satisfies a typical L1- L∞ dispersive estimate of the form
‖eitL‖L1→L∞≲|t|-n/2.
Then we prove a similar L1- L∞ dispersive estimate for a general class of flows eitϕ(L), with φ(r) of power type near 0 and near ∞. In the case of fractional powers φ(L) = Lν, ν∈ (0 , 1) , we deduce dispersive estimates for eitLν with data in Sobolev, Besov or Hardy spaces HLp with p∈ (0 , 1] , associated to the operator L.
Original language | English |
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Pages (from-to) | 1393-1426 |
Number of pages | 34 |
Journal | Mathematische Annalen |
Volume | 375 |
Issue number | 3-4 |
Early online date | 15 Jun 2019 |
DOIs | |
Publication status | Published - Dec 2019 |
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Dive into the research topics of 'On the flows associated to selfadjoint operators on metric measure spaces'. Together they form a unique fingerprint.Projects
- 1 Finished
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Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals
Duong, X., Ward, L., Li, J., Lacey, M., Pipher, J. & MQRES, M.
16/02/16 → 30/06/20
Project: Research