Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure (Paperback, 2023)

Chapter. 1.?Introduction and main results.- Chapter. 2.?Preliminaries on function spaces.- Chapter. 3.?Preliminaries on operator theory.- Chapter. 4.?Hp - Hq bounded families.- Chapter. 5.?Conservation properties.- Chapter. 6.?The four critical numbers.- Chapter. 7.?Riesz transform estimates: Part I.- Chapter. 8.?Operator-adapted spaces.- Chapter. 9.?Identification of adapted Hardy spaces.- Chapter. 10.?A digression: H -calculus and analyticity.- Chapter. 11.?Riesz transform estimates: Part II.- Chapter. 12.?Critical numbers for Poisson and heat semigroups.- Chapter. 13.?Lp boundedness of the Hodge projector.- Chapter. 14.?Critical numbers and kernel bounds.- Chapter. 15.?Comparison with the Auscher-Stahlhut interval.- Chapter. 16.?Basic properties of weak solutions.- Chapter. 17.?Existence in Hp Dirichlet and Regularity problems.- Chapter. 18. Existence in the Dirichlet problems with?data.- Chapter. 19.?Existence in Dirichlet problems with fractional regularity?data.- Chapter. 20.?Single layer operators for L and estimates for L-1.- Chapter. 21.?Uniqueness in regularity and Dirichlet problems.- Chapter. 22.?The Neumann problem.- Appendix A.?Non-tangential maximal functions and traces.- Appendix B.?The Lp-realization of a sectorial operator in L2.- References.- Index.