Quadratic estimates for perturbed Dirac type operators on doubling   measure metric spaces
  We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate. 
Lashi Bandara
math.SP