Some new function spaces and their applications to harmonic analysis. (English) Zbl 0569.42016

This paper is devoted to the definition of a new family of function spaces and to the investigation of their fundamental properties. These spaces, called “tent spaces” are of functions on \(X\times {\mathbb{R}}_+\) where X is a Euclidean space and the spaces are so defined that the functions have “good” boundary values on the boundary \(X\) of this space. Such boundary values play a central role in harmonic analysis and the theory developed in this paper systemises a great deal of the earlier work. It is so rich in material that it is hardly possible in a short review to summarize the results in detail. To show the range of these methods the authors give a number of applications at the close of this paper, to maximal functions, to the Hilbert transform and to the theory of Hardy spaces.
Reviewer: S. J. Patterson


42B25 Maximal functions, Littlewood-Paley theory
31B25 Boundary behavior of harmonic functions in higher dimensions
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