Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Notation and preliminaries -- 2.1. Spaces of homogeneous type -- 2.2. Assumptions -- 2.3. The classical Hardy space H1(Rn) -- 2.4. Hardy spaces via atoms -- 2.5. Hardy spaces via molecules -- 2.6. Hardy spaces via square and maximal functions -- 2.7. BMO spaces associated to operators -- 2.8. Historical notes -- Chapter 3. Davies-Gaffney estimates -- 3.1. Self-improving properties of Davies-Gaffney estimates -- 3.2. Finite speed propagation for the wave equation and Davies-Gaffney estimates -- Chapter 4. The decomposition into atoms -- 4.1. Strategy of the proof of Theorem 4.1 -- 4.2. H1L,at, M(X) H1L, Sh(X) H2(X) for all M&gt -- n0/4 -- 4.3. The inclusion ( H1L, Sh(X) H2(X))H1L,at, M(X) for all M1 -- 4.4. Equivalence of H1L, SP(X) and H1L,at, M(X) when M&gt -- n0/4 -- 4.5. Inclusion among the spaces H1L,at, M(X), H1L, Nh(X) and H1L, NP(X) -- Chapter 5. Relations between atoms and molecules -- Chapter 6. BMOL,M(X): Duality with Hardy spaces -- Chapter 7. Hardy spaces and Gaussian estimates -- 7.1. Hardy spaces H1L,at, M(X), H1L, Sh(X) and H1L, SP(X) and Gaussian estimates -- 7.2. Hardy spaces via maximal functions -- 7.3. The spaces BMOL(X) under Gaussian bounds -- Chapter 8. Hardy spaces associated to Schrödinger operators -- 8.1. Equivalences among H1L,at, M(Rn), H1L, Sh(Rn) and H1L, SP(Rn) -- 8.2. Maximal characterization of H1L,at, M(Rn) -- 8.3. H1L,at,MH1 bounds for Riesz transforms of Schrödinger operators -- Chapter 9. Further properties of Hardy spaces associated to operators -- 9.1. The semigroup with the conservation property -- 9.2. Hardy spaces HpL(X) for 1p&lt -- -- Bibliography.

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