Morrey and Campanato Meet Besov, Lizorkin and Triebel

During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞. Front Matter....Pages i-xi Introduction....Pages 1-19 The Spaces $$B_{p, q}^{s, \tau }({\mathbb{R}}^ n)$$ and $$F_{p, q}^{s, \tau }({\mathbb{R}}^ n)$$ ....Pages 21-48 Almost Diagonal Operators and Atomic and Molecular Decompositions....Pages 49-64 Several Equivalent Characterizations....Pages 65-135 Pseudo-Differential Operators....Pages 137-146 Key Theorems....Pages 147-175 Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces....Pages 177-250 Homogeneous Spaces....Pages 251-269 Back Matter....Pages 271-288