Cruz-Uribe, David; Forzani, Liliana; Maldonado, Diego The structure of increasing weights on the real line. (English) Zbl 1177.46019 Houston J. Math. 34, No. 3, 951-983 (2008). The structure of a variety of related weight classes on the real line and the positive real axis is examined: doubling measures, \(A_p\) weights, the \(B_p\) weights of Ariño and Muckenhoupt, and \(\Delta_2\) Young functions. A number of characterizations of these classes are given: as applications, the Matuszewska-Orlicz indices of the Young function \(w(t)=t^{a+b\sin(\log(|\log(t)|))}\), \(a,b\in \mathbb{R}^+\), \(a>1+b\sqrt{2}\), due to Linderberg is computed, a sufficient condition for a function \(m\) to be a multiplier of the doubling measures on \(\mathbb{R}^+\) is given, and a function \(W\) on \(\mathbb{R}^+\) is constructed such that \(W(0)=0\), \(W\) is increasing and locally Hölder continuous, but the measure \(\mu\) defined by \(\mu([0,t])=W(t)\) is not a doubling measure. Reviewer: Giorgi Oniani (Kutaisi) Cited in 3 Documents MSC: 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 42B25 Maximal functions, Littlewood-Paley theory Keywords:weights; Young functions; doubling measures; Matuszewska-Orlicz indices Citations:Zbl 0716.42016 PDFBibTeX XMLCite \textit{D. Cruz-Uribe} et al., Houston J. Math. 34, No. 3, 951--983 (2008; Zbl 1177.46019) Full Text: Link