Multivariate spectral multipliers for systems of Ornstein–Uhlenbeck operators

Tom 216 / 2013

Błażej Wróbel Studia Mathematica 216 (2013), 47-67 MSC: Primary 42B15; Secondary 42C10; Tertiary 47A60. DOI: 10.4064/sm216-1-4

Streszczenie

Multivariate spectral multipliers for systems of Ornstein–Uhlenbeck operators are studied. We prove that $L^p$-uniform, $1< p< \infty ,$ spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on $p.$ We also characterize $L^1$-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.

Autorzy

  • Błażej WróbelInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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