Functions of a second order elliptic operator in rearrangement invariant spaces

The functional calculus of positive operators is applied to second-order elliptic operatorsP. For any absolutely concave (t), the corresponding operators (P ^–1) are represented as integral operators, their kernels are estimated, and these estimates are used for studying (P ^–1) in Lorentz, Marcinkiewicz and Orlicz spaces. Most of results obtained are sharp.