Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu; Dachun Yang

Guoen Hu ; Dachun Yang

Studia Mathematica, Tome 187 (2008), p. 101-123 / Harvested from The Polish Digital Mathematics Library

Résumé

Let μ be a nonnegative Radon measure on $ℝ^{d}$ which satisfies μ(B(x,r)) ≤ Crⁿ for any $x \in ℝ^{d}$ and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with $A_{p}^{ϱ} (μ)$ weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with $A_{\infty}^{ϱ} (μ)$ weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).

Publié le : 2008-01-01

Zbl 1283.42023

EUDML-ID : urn:eudml:doc:284902

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     title = {Weighted norm inequalities for maximal singular integrals with nondoubling measures},
     journal = {Studia Mathematica},
     volume = {187},
     year = {2008},
     pages = {101-123},
     zbl = {1283.42023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-1}
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Guoen Hu; Dachun Yang. Weighted norm inequalities for maximal singular integrals with nondoubling measures. Studia Mathematica, Tome 187 (2008) pp. 101-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-1/