Weighted estimates for operator-valued Fourier multipliers

Weighted estimates for operator-valued Fourier multipliers

We establish Littlewood–Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem for operator-valued multipliers. We also show two-weight estimates for multipliers satisfying Hörmander type conditions....

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Veröffentlicht in:Collectanea mathematica (Barcelona) 2020-09, Vol.71 (3), p.511-548
Hauptverfasser: Fackler, Stephan, Hytönen, Tuomas P., Lindemulder, Nick
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Multipliers
Weight
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Zusammenfassung:We establish Littlewood–Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem for operator-valued multipliers. We also show two-weight estimates for multipliers satisfying Hörmander type conditions.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-019-00275-0