Contents Chapter 1. Main results 1 1 Frame decompositions 2 2 Molecular boundedness and operator decompositions 9 3 Molecules and the affine group 11 Chapter 2. Molecular decompositions of operators 14 1 Smooth C alderon-Zygmund operators 14 2 Cotlar type operators 18 3 Kernel estimates 25 4 Boundedness on spaces of molecules 29 5 Triebel-Lizorkin spaces 39 Chapter 3. Frames 43 1 Continuity of group action 43 2 Inversion of frame operator 44 3 Convergence in Triebel-Lizorkin spaces 46 4 Algebras of singular integral operators 48 Chapter 4. Maximal theorems and equi-convergence 53 1 Introduction 53 2 Equiconvergence 54 3 Almost everywhere convergence of wavelet frame expansions 63 4 Affine approximations to the identity 66 Appendix Proof of Basic Estimates 70
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