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 = .

A new general framework unifying Besov-Triebel-Lizorkin spaces, Morrey spaces, Campanato spaces and Q spaces is established In the key theorems characterizations by atoms, molecules, wavelets, differences and oscillations are given Special cases of these new scales (namely Besov-Triebel-Lizorkin spaces built on Morrey spaces) have been shown to be useful in the study of Navier-Stokes equations Includes supplementary material: sn.pub/extras

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