$A_p$ weights for nondoubling measures in $R^n$ and applications
نویسندگان
چکیده
منابع مشابه
Ap WEIGHTS FOR NONDOUBLING MEASURES IN R AND APPLICATIONS
We study an analogue of the classical theory of Ap(μ) weights in Rn without assuming that the underlying measure μ is doubling. Then, we obtain weighted norm inequalities for the (centered) Hardy-Littlewood maximal function and corresponding weighted estimates for nonclassical CalderónZygmund operators. We also consider commutators of those CalderónZygmund operators with bounded mean oscillatio...
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1. Introduction. The Calderón-Zygmund theory of singular integrals has been traditionally considered with respect to a measure satisfying a doubling condition. Recently, Tolsa [T] and, independently, Nazarov, Treil, and Volberg [NTV] have shown that this standard doubling condition was not really necessary. Likewise, in the homogeneous spaces setting, functions of bounded mean oscillation, BMO,...
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A well known result proved by F. John for 0 < λ < 1/2 and by J.-O. Strömberg for λ = 1/2 states that ‖f‖BMO(ω) sup Q inf c∈R inf{α > 0 : ω{x ∈ Q : |f(x)− c| > α} < λω(Q)} for any measure ω satisfying the doubling condition. In this note we extend this result to all absolutely continuous measures. In particular, we show that Strömberg’s “1/2-phenomenon” still holds in the nondoubling case. An im...
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Let μ be a nonnegative Radon measure on R which only satisfies the following growth condition that there exists a positive constant C such that μ B x, r ≤ Cr for all x ∈ R, r > 0 and some fixed n ∈ 0, d . In this paper, the authors prove that for suitable indexes ρ and λ, the parametrized g∗ λ function M∗,ρ λ is bounded on L μ for p ∈ 2,∞ with the assumption that the kernel of the operator M∗,ρ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-02922-7