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Keywords:
non-doubling measure; $\mathop{\rm RBMO}(\mu )$; sharp maximal function
non-doubling measure; $\mathop{\rm RBMO}(\mu )$; sharp maximal function
Summary:
Let $\mu $ be a nonnegative Radon measure on ${{\mathbb R}^d}$ which only satisfies $\mu (B(x, r))\le C_0r^n$ for all $x\in {{\mathbb R}^d}$, $r>0$, with some fixed constants $C_0>0$ and $n\in (0,d].$ In this paper, a new characterization for the space $\mathop{\rm RBMO}(\mu )$ of Tolsa in terms of the John-Strömberg sharp maximal function is established.
References:
[1] Hu, G., Wang, X., Yang, D.: A new characterization for regular BMO with non-doubling measures. Proc. Edinburgh Math. Soc. 51 (2008), 155-170. MR 2391636 | Zbl 1138.42012
[2] Hu, G., Yang, D.: Weighted norm inequalities for maximal singular integrals with non-doubling measures. Studia Math. 187 (2008), 101-123. DOI 10.4064/sm187-2-1 | MR 2413311
[3] John, F.: Quasi-isometric mappings. 1965 Seminari 1962/63 Anal. Alg. Geom. e Topol., vol. 2, Ist. Naz. Alta Mat., 462-473, Ediz. Cremonese, Rome. MR 0190905 | Zbl 0263.46006
[4] Lerner, A. K.: On the John-Strömberg characterization of BMO for nondoubling measures. Real Anal. Exch. 28 (2002/03), 649-660. DOI 10.14321/realanalexch.28.2.0649 | MR 2010347 | Zbl 1044.42018
[5] Mateu, J., Mattila, P., Nicolau, A., Orobitg, J.: BMO for nondoubling measures. Duke Math. J. 102 (2000), 533-565. DOI 10.1215/S0012-7094-00-10238-4 | MR 1756109 | Zbl 0964.42009
[6] Meng, Y.: Multilinear Calderón-Zygmund operators on the product of Lebesgue spaces with non-doubling measures. J. Math. Anal. Appl. 335 (2007), 314-331. DOI 10.1016/j.jmaa.2007.01.075 | MR 2340323 | Zbl 1121.42012
[7] Nazarov, F., Treil, S., Volberg, A.: The $Tb$-theorem on non-homogeneous spaces. Acta Math. 190 (2003), 151-239. DOI 10.1007/BF02392690 | MR 1998349 | Zbl 1065.42014
[8] Strömberg, J. O.: Bounded mean oscillation with Orlicz norms and duality of Hardy spaces. Indiana Univ. Math. J. 28 (1979), 511-544. DOI 10.1512/iumj.1979.28.28037 | MR 0529683
[9] Tolsa, X.: $BMO$, $H^1$ and Calderón-Zygmund operators for non doubling measures. Math. Ann. 319 (2001), 89-149. DOI 10.1007/PL00004432 | MR 1812821
[10] Tolsa, X.: Painlevé's problem and the semiadditivity of analytic capacity. Acta Math. 190 (2003), 105-149. DOI 10.1007/BF02393237 | MR 1982794 | Zbl 1060.30031
[11] Tolsa, X.: The semiadditivity of continuous analytic capacity and the inner boundary conjecture. Am. J. Math. 126 (2004), 523-567. DOI 10.1353/ajm.2004.0021 | MR 2058383 | Zbl 1060.30032
[12] Tolsa, X.: Analytic capacity and Calderón-Zygmund theory with non doubling measures. Seminar of Mathematical Analysis, 239-271, {Colecc. Abierta}, {\it 71}, Univ. Sevilla Secr. Publ., Seville. (2004). MR 2117070
[13] Tolsa, X.: Bilipschitz maps, analytic capacity, and the Cauchy integral. Ann. Math. 162 (2005), 1243-1304. DOI 10.4007/annals.2005.162.1243 | MR 2179730 | Zbl 1097.30020
[14] Tolsa, X.: Painlevé's problem and analytic capacity. Collect. Math. Extra (2006), 89-125. MR 2264206 | Zbl 1105.30015
[15] Verdera, J.: The fall of the doubling condition in Calderón-Zygmund theory. Publ. Mat. Extra (2002), 275-292. DOI 10.5565/PUBLMAT_Esco02_12 | MR 1964824 | Zbl 1025.42008
[16] Volberg, A.: Calderón-Zygmund capacities and operators on nonhomogeneous spaces {CBMS Regional Conference Series in Mathematics}, {\it 100}, Amer. Math. Soc., Providence, RI. (2003). MR 2019058
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