Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces (Paperback)

Introduction Preliminaries on capacities Localization of Newton and Riesz potentials From distribution to measure. Carleson property Potential neighborhood that has properties (3.13)-(3.14) The tree of the proof The first reduction to nonhomogeneous $Tb$ theorem The second reduction The third reduction The fourth reduction The proof of nonhomogeneous Cotlar's lemma. Arbitrary measure Starting the proof of nonhomogeneous nonaccretive $Tb$ theorem Next step in theorem 10.6. Good and bad functions Estimate of the diagonal sum. Remainder in theorem 3.3 Two-weight estimate for the Hilbert transform. Preliminaries Necessity in the main theorem Two-weight Hilbert transform. Towards the main theorem Long range interaction The rest of the long range interaction The short range interaction Difficult terms and several paraproducts Two-weight Hilbert transform and maximal operator Bibliography.