On Necessary And Sufficient Conditions For Lp-Estimates Of Riesz Transforms Associated To Elliptic Operators On Rn And Related Estimates

Focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form its semi group, the gradient of the semi group, functional calculus, square functions and Riesz transforms. This book introduces four numbers associated to the semi group and its gradient that completely rule the ranges of exponents for the $L^p$ estimates.