Geodesic
On the maximal function for rotation invariant measures in $ℝ^{n}$
Studia Mathematica, Tome 110 (1994) no. 1, pp. 9-17 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given a positive measure μ in $ℝ^n$, there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ}f(x) = sup_{x ∈ B} 1/μ(B) ʃ_{B} |f|dμ$, where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^n$. We give some necessary and sufficient conditions for $M_μ$ to be bounded from $L^{1}(dμ)$ to $L^{1,∞}(dμ)$.
DOI : 10.4064/sm-110-1-9-17
Keywords: maximal operators, weak type estimates 
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Ana M. Vargas. On the maximal function for rotation invariant measures in $ℝ^{n}$. Studia Mathematica, Tome 110 (1994) no. 1, pp. 9-17. doi: 10.4064/sm-110-1-9-17

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