On the flows associated to selfadjoint operators on metric measure spaces

The Anh Bui, Piero D'Ancona, Xuan Thinh Duong, Detlef Müller

Research output: Contribution to journalArticleResearchpeer-review

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

‖eitLL1→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.

LanguageEnglish
Pages1393-1426
Number of pages34
JournalMathematische Annalen
Volume375
Issue number3-4
Early online date15 Jun 2019
DOIs
Publication statusPublished - Dec 2019

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Dispersive Estimates
Metric Measure Space
Self-adjoint Operator
Doubling Measure
Fractional Powers
Besov Spaces
Hardy Space
Sobolev Spaces
Metric space
Deduce
Ball
Non-negative
Radius
Upper bound
Operator

Cite this

Bui, The Anh ; D'Ancona, Piero ; Duong, Xuan Thinh ; Müller, Detlef. / On the flows associated to selfadjoint operators on metric measure spaces. In: Mathematische Annalen. 2019 ; Vol. 375, No. 3-4. pp. 1393-1426.
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On the flows associated to selfadjoint operators on metric measure spaces. / Bui, The Anh; D'Ancona, Piero; Duong, Xuan Thinh; Müller, Detlef.

In: Mathematische Annalen, Vol. 375, No. 3-4, 12.2019, p. 1393-1426.

Research output: Contribution to journalArticleResearchpeer-review

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