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

Vargas, Ana

On the maximal function for rotation invariant measures in

ℝ^{n}

Vargas, Ana

Studia Mathematica, Tome 108 (1994), p. 9-17 / Harvested from The Polish Digital Mathematics Library

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Résumé

Given a positive measure μ in $ℝ^{n}$ , there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ} f (x) = s u p_{x \in B} 1 / μ (B) ʃ_{B} | f | d μ$ , 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 $L^{1} (d μ)$ to $L^{1, \infty} (d μ)$ .

Publié le : 1994-01-01

Zbl 0818.42009

EUDML-ID : urn:eudml:doc:216102

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     author = {Ana Vargas},
     title = {On the maximal function for rotation invariant measures in $$\mathbb{R}$^{n}$
            },
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {9-17},
     zbl = {0818.42009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv110i1p9bwm}
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Vargas, Ana. On the maximal function for rotation invariant measures in $ℝ^{n}$
            . Studia Mathematica, Tome 108 (1994) pp. 9-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv110i1p9bwm/

Bibliographie

[00000] [M-S] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. | Zbl 0139.29002

[00001] [S] P. Sjögren, A remark on the maximal function for measures in $ℝ^{n}$ , Amer. J. Math. 105 (1983), 1231-1233.