منابع مشابه
Bmo for Nondoubling Measures
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,...
متن کاملOn the John-strömberg Characterization of Bmo for Nondoubling Measures
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...
متن کاملAp 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...
متن کاملBoundedness of Parametrized Littlewood-Paley Operators with Nondoubling Measures
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...
متن کاملResearch Article Uniform Boundedness for Approximations of the Identity with Nondoubling Measures
Let μ be a nonnegative Radon measure on Rd which satisfies the growth condition that there exist constants C0 > 0 and n∈ (0,d] such that for all x ∈Rd and r > 0, μ(B(x,r))≤ C0r, where B(x,r) is the open ball centered at x and having radius r. In this paper, the authors establish the uniform boundedness for approximations of the identity introduced by Tolsa in the Hardy space H1(μ) and the BLO-t...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2000
ISSN: 0026-2285
DOI: 10.1307/mmj/1030132594