Rubio de Francia, José L. Factorization theory and \(A_p\) weights. (English) Zbl 0558.42012 Am. J. Math. 106, 533-547 (1984). In a series of papers, culminating with the paper under review, the author has developed a new and powerful approach to the theory of weighted norm inequality with \(A_ p\) weights [see Proc. Am. Math. Soc. 83, 673–679 (1981; Zbl 0477.42011); Lect. Notes Math. 908, 86–101 (1982; Zbl 0191.42019)]. The central idea in this approach is the use of the theory of factorization of operators developed by B. Maurey. The results obtained are nothing less than spectacular. For example, the factorization theorem of P. W. Jones [Ann. Math. (2) 111, 511–530 (1980; Zbl 0493.42030)] which was previously available through complicated “hard analysis” is reduced to a piece of basic abstract nonsense. It was pointed out by P. Jones (loc. cit.) that his factorization theorem could be used to interpolate weighted \(A_ p\) norm inequalities in the expected way. A remarkable result proved in this paper is that \(A_ p\) norm inequalities need not be interpolated since they can be extrapolated. For example, a particular case of the extrapolation theorem of Rubio de Francia states that if for a fixed \(p\), the operator \(T\) is bounded in \(L^ p(w)\) for all \(w\in A_ p\), then \(T\) is bounded in \(L^ q(w)\) for every \(w\in A_ p\), \(1<q<\infty\). Reviewer: M. Milman Cited in 9 ReviewsCited in 145 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory 46E40 Spaces of vector- and operator-valued functions Keywords:weighted norm inequality with \(A_ p\) weights; factorization of operators Citations:Zbl 0477.42011; Zbl 0191.42019; Zbl 0493.42030 × Cite Format Result Cite Review PDF Full Text: DOI