Fefferman, Robert; Soria, Fernando The space weak \(H^ 1\). (English) Zbl 0626.42013 Stud. Math. 85, 1-16 (1986). Let \(\psi\) be a function in \(C_ c^{\infty}({\mathbb{R}}^ n)\) with non- zero integral and let for \(t>0\), \(\psi_ t(x)=t^{-n}\psi (x/t).\) For a distribution in \({\mathbb{R}}^ n\), define the maximal operator \(f^*(x)=\sup_{t>0}| f*\psi_ t(x)|.\) The authors study in detail the space weak \(H^ 1=\{f/f^*\in weak L^ 1\}\). In particular they show how to obtain atomic decompositions of distributions in weak \(H^ 1\). They also provide several interesting applications to harmonic analysis. Reviewer: M.Milman Cited in 6 ReviewsCited in 57 Documents MSC: 42B30 \(H^p\)-spaces 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46M35 Abstract interpolation of topological vector spaces Keywords:maximal operator; weak \(H^ 1\); applications to harmonic analysis PDFBibTeX XMLCite \textit{R. Fefferman} and \textit{F. Soria}, Stud. Math. 85, 1--16 (1986; Zbl 0626.42013) Full Text: DOI EuDML