Functional calculus, regularity and Riesz transforms of weighted subcoercive operators on sigma-finite measure spaces (original) (raw)

If H is an n-th order weighted subcoercive operator associated to a continuous representation U of a d-dimensional connected Lie group G in Lp(M; fL), where p E (1,00) and (M; fL) is a O"-finite measure space, then we show that vI + H has a bounded Hoc> functional calculus if Re v is large enough. Moreover, the domain D((vI + H)m/n) of the fractional power equals the space of m times differentiable vectors in Lp-sense if Re v is large enough and m is in a suitable subset of [0,00). Finally, we deduce kernel bounds for reduced operator kernels of Riesz transforms and functional operators of strongly elliptic operators on homogeneous spaces.