$H^{\infty }$ calculus for submarkovian semigroups on weighted $L^2$ spaces

Komla Domelevo, Christoph Kriegler, Stefanie Petermichl

Let $(T_t{)}_{t\ge 0}$ 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(Σ_θ)…