Search results for "commutators"
showing 2 items of 2 documents
Commutators, C0-semigroups and resolvent estimates
2004
Abstract We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C 0 -semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [ H ,i A ] is not comparable to H . The applications include the spectral theory of zero mass quantum field models.
Off-diagonal estimates for bi-parameter commutators
2022
Tutkimme kahden parametrin singulaari-integraalien kommutaattoreiden rajoit-tuneisuutta iteroitujen avaruuksien[b, T]:Lp1Lp2→Lq1Lq2välillä kunqi, pi∈(1,∞)ja erityisesti fraktionaalisessa tilanteessaqi6=pi. Yhteensä seitsemässä ta-pauksessa yhdeksästä saavutamme täyden karaterisoinnin rajoittuneisuudella symboliabkoskevillaoskillatorisilla testiehdoilla. We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces [b,T]:Lp1Lp2→Lq1Lq2 in the off-diagonal situation qi,pi∈(1,∞) where we allow qi≠pi. Boundedness is fully characterized in terms of oscillatory testing conditions on the function b for a total seven out of the nine possible arrangements of the inte…