Coifman--Latter Atomic Decomposition Analysis Riesz Representation Theorem Functional Analysis Canonical Isomorphism $\dot{H}^0 \cong L^2$ Sobolev Spaces Recovery of Classical Sobolev Spaces Sobolev Spaces Fundamental Theorem of Algebra Complex Analysis Adjoint Operator Norm Inequality Functional Analysis Compactness In BV Geometric Measure Theory Bounded Diagonal Operators Functional Analysis Analysis Area Functional Analysis Subarea