A new characterization of RBMO ( μ ) by John-Strömberg sharp maximal functions

Guoen Hu; Dachun Yang; Dongyong Yang

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 1, page 159-171
  • ISSN: 0011-4642

Abstract

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Let μ be a nonnegative Radon measure on ℝ d which only satisfies μ ( B ( x , r ) ) ≤ C 0 r n for all x ∈ ℝ d , r > 0 , with some fixed constants C 0 > 0 and n ∈ ( 0 , d ] . In this paper, a new characterization for the space RBMO ( μ ) of Tolsa in terms of the John-Strömberg sharp maximal function is established.

How to cite

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Hu, Guoen, Yang, Dachun, and Yang, Dongyong. "A new characterization of ${\rm RBMO}(\mu )$ by John-Strömberg sharp maximal functions." Czechoslovak Mathematical Journal 59.1 (2009): 159-171. <http://eudml.org/doc/37914>.

@article{Hu2009,
abstract = {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.},
author = {Hu, Guoen, Yang, Dachun, Yang, Dongyong},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-doubling measure; $\mathop \{\rm RBMO\}(\mu )$; sharp maximal function; non-doubling measure; ; sharp maximal function},
language = {eng},
number = {1},
pages = {159-171},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new characterization of $\{\rm RBMO\}(\mu )$ by John-Strömberg sharp maximal functions},
url = {http://eudml.org/doc/37914},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Hu, Guoen
AU - Yang, Dachun
AU - Yang, Dongyong
TI - A new characterization of ${\rm RBMO}(\mu )$ by John-Strömberg sharp maximal functions
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 159
EP - 171
AB - 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.
LA - eng
KW - non-doubling measure; $\mathop {\rm RBMO}(\mu )$; sharp maximal function; non-doubling measure; ; sharp maximal function
UR - http://eudml.org/doc/37914
ER -

References

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  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. (2008) Zbl1138.42012MR2391636
  2. Hu, G., Yang, D., 10.4064/sm187-2-1, Studia Math. 187 (2008), 101-123. (2008) MR2413311DOI10.4064/sm187-2-1
  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. Zbl0263.46006MR0190905
  4. Lerner, A. K., 10.14321/realanalexch.28.2.0649, Real Anal. Exch. 28 (2002/03), 649-660. Zbl1044.42018MR2010347DOI10.14321/realanalexch.28.2.0649
  5. Mateu, J., Mattila, P., Nicolau, A., Orobitg, J., 10.1215/S0012-7094-00-10238-4, Duke Math. J. 102 (2000), 533-565. (2000) Zbl0964.42009MR1756109DOI10.1215/S0012-7094-00-10238-4
  6. Meng, Y., 10.1016/j.jmaa.2007.01.075, J. Math. Anal. Appl. 335 (2007), 314-331. (2007) Zbl1121.42012MR2340323DOI10.1016/j.jmaa.2007.01.075
  7. Nazarov, F., Treil, S., Volberg, A., 10.1007/BF02392690, Acta Math. 190 (2003), 151-239. (2003) Zbl1065.42014MR1998349DOI10.1007/BF02392690
  8. Strömberg, J. O., 10.1512/iumj.1979.28.28037, Indiana Univ. Math. J. 28 (1979), 511-544. (1979) MR0529683DOI10.1512/iumj.1979.28.28037
  9. Tolsa, X., 10.1007/PL00004432, Math. Ann. 319 (2001), 89-149. (2001) MR1812821DOI10.1007/PL00004432
  10. Tolsa, X., 10.1007/BF02393237, Acta Math. 190 (2003), 105-149. (2003) Zbl1060.30031MR1982794DOI10.1007/BF02393237
  11. Tolsa, X., 10.1353/ajm.2004.0021, Am. J. Math. 126 (2004), 523-567. (2004) Zbl1060.30032MR2058383DOI10.1353/ajm.2004.0021
  12. Tolsa, X., Analytic capacity and Calderón-Zygmund theory with non doubling measures. Seminar of Mathematical Analysis, 239-271, Colecc. Abierta, 71, Univ. Sevilla Secr. Publ., Seville, (2004). (2004) MR2117070
  13. Tolsa, X., 10.4007/annals.2005.162.1243, Ann. Math. 162 (2005), 1243-1304. (2005) Zbl1097.30020MR2179730DOI10.4007/annals.2005.162.1243
  14. Tolsa, X., Painlevé's problem and analytic capacity, Collect. Math. Extra (2006), 89-125. (2006) Zbl1105.30015MR2264206
  15. Verdera, J., 10.5565/PUBLMAT_Esco02_12, Publ. Mat. Extra (2002), 275-292. (2002) Zbl1025.42008MR1964824DOI10.5565/PUBLMAT_Esco02_12
  16. Volberg, A., Calderón-Zygmund capacities and operators on nonhomogeneous spaces CBMS Regional Conference Series in Mathematics, 100, Amer. Math. Soc., Providence, RI, (2003). (2003) MR2019058

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