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- W4288093998 abstract "Let $(T_t)_{t geq 0}$ be a markovian (resp. submarkovian) semigroup on some $sigma$-finite measure space $(Omega,mu)$. We prove that its negative generator $A$ has a bounded $H^infty(Sigma_theta)$ calculus on the weighted space $L^2(Omega,wdmu)$ as long as the weight $w : Omega to (0,infty)$ has finite characteristic defined by $Q^A_2(w) = sup_{t > 0} left| T_t(w) T_t left(w^{-1} right) right|_{L^infty(Omega)}$ (resp. by a variant for submarkovian semigroups). Some additional technical conditions on the semigroup have to be imposed and their validity in examples is discussed. Any angle $theta > frac{pi}{2}$ is admissible in the above $H^infty$ calculus, and for some semigroups also certain $theta = theta_w < frac{pi}{2}$ depending on the size of $Q^A_2(w)$. The norm of the $H^infty(Sigma_theta)$ calculus is linear in the $Q^A_2$ characteristic for $theta > frac{pi}{2}$. We also discuss negative results on angles $theta < frac{pi}{2}$. Namely we show that there is a markovian semigroup on a probability space and a $Q^A_2$ weight $w$ without Hormander functional calculus on $L^2(Omega,w dmu)$." @default.
- W4288093998 created "2022-07-28" @default.
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- W4288093998 date "2019-10-08" @default.
- W4288093998 modified "2023-09-29" @default.
- W4288093998 title "$H^infty$ calculus for submarkovian semigroups on weighted $L^2$ spaces" @default.
- W4288093998 hasPublicationYear "2019" @default.
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