On the maximal function for rotation invariant measures in $ℝ^{n}$

Tom 110 / 1994

Ana M. Vargas Studia Mathematica 110 (1994), 9-17 DOI: 10.4064/sm-110-1-9-17


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 $L^{1,∞}(dμ)$.


  • Ana M. Vargas

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