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The space weak H 1 . (English) Zbl 0626.42013
Let ψ be a function in C c ( n ) with non- zero integral and let for t>0, ψ t (x)=t -n ψ(x/t)· For a distribution in n , define the maximal operator f * (x)=sup t>0 |f*ψ t (x)|· The authors study in detail the space weak H 1 ={f/f * weakL 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

42B30H p -spaces (Fourier analysis)
46E30Spaces of measurable functions
46M35Abstract interpolation of topological linear spaces