Abstract
Many fields in analysis require the study of specific function spaces. In harmonic analysis the Lebesgue spaces LP, the Hardy spaces HP, various forms of Lipschitz spaces and the space BMO are important. Similarly, the Sobolev spaces L k P are basic in the study of partial differential equations. From the original definitions of these spaces, it may not appear that they are closely related. There are, however, various unified approaches to their study. The Littlewood-Paley theory provides one of the most successful unifying perspectives on these and other function spaces.
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