Functional calculus for generators of symmetric contraction semigroups

Abstract

We prove that every generator of a symmetric contraction semigroup on a $\sigma$-finite measure space admits, for $1<p<\infty$, a Hörmander-type holomorphic functional calculus on $L^p$ in the sector of angle ${\varphi }_p^{\ast }=\arcsin |1-2/p|$. The obtained angle is optimal.

26 pages, minor corrections and slight changes of notation. Some changes in Sections 4, 6 and 7

References in corpus (1)

• Sharp $L^p$ estimates for discrete second order {R}iesz transforms

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