The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator.  Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems:  the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions. weiterlesen