Frontiers of Mathematics in China >
An equivalent characterization of BMO with Gauss measure
Received date: 07 May 2016
Accepted date: 16 Dec 2016
Published date: 20 Apr 2017
Copyright
Let γbe the Gauss measure on ℝn.We establish a Calderón-Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.
Zhehui WANG , Dongyong YANG . An equivalent characterization of BMO with Gauss measure[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 749 -768 . DOI: 10.1007/s11464-017-0624-5
| 1 |
BuiT A, DuongX T. Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces. J Geom Anal, 2011, 23: 895–932
|
| 2 |
CoifmanR R, WeissG. Analyse Harmonique Non-commutative sur Certains Espaces Homogènes. Étude de certaines intégrales singulières. Lecture Notes in Math, Vol 242. Berlin-New York: Springer-Verlag, 1971
|
| 3 |
DuongX T, LiJ, MaoS, WuH, YangD. Compactness of Riesz transform commutator associated with Bessel operators. J Anal Math (to appear)
|
| 4 |
FabesE B, GutíerrezC, ScottoR. Weak type estimates for the Riesz transforms associated with the Gaussian measure. Rev Mat Iberoam, 1994, 10: 229–281
|
| 5 |
García-CuervaJ, MauceriG, MedaS, SjögrenP, TorreaJ L. Functional calculus for the Ornstein-Uhlenbeck operator. J Funct Anal, 2001, 183: 413–450
|
| 6 |
García-CuervaJ, MauceriG, MedaS, SjögrenP, TorreaJ L. Maximal operators for the holomorphic Ornstein-Uhlenbeck semigroup. J Lond Math Soc (2), 2003, 67: 219–234
|
| 7 |
GundyR F. Sur les transformations de Riesz pour le semi-groupe dÓrnstein-Uhlenbeck. C R Acad Sci Paris Sér I Math, 1986, 303: 967–970
|
| 8 |
GutíerrezC E. On the Riesz transforms for Gaussian measures. J Funct Anal, 1994, 120: 107–134
|
| 9 |
HebischW, MauceriG, MedaS. Holomorphy of spectral multipliers of the Ornstein-Uhlenbeck operator. J Funct Anal, 2004, 210: 101–124
|
| 10 |
HuG, MengY, YangD. A new characterization of regularized BMO spaces on nonhomogeneous spaces and its applications. Ann Acad Sci Fenn Math, 2013, 38: 3–27
|
| 11 |
HuG, YangDa, YangDo. A new characterization of RBMO(μ) by John-Strömberg sharp maximal functions. Czechoslovak Math J, 2009, 59(134): 159–171
|
| 12 |
HytönenT. A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. Publ Mat, 2010, 54: 485–504
|
| 13 |
HytönenT, MartikainenH. Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces. J Geom Anal, 2012, 22: 1071–1107
|
| 14 |
HytönenT, YangDa, YangDo. The Hardy space H1 on non-homogeneous metric spaces. Math Proc Cambridge Philos Soc, 2012, 153: 9–31
|
| 15 |
JawerthB, TorchinskyA. Local sharp maximal functions. J Approx Theory, 1985, 43: 231–270
|
| 16 |
JohnF, NirenbergL. On functions of bounded mean oscillation. Comm Pure Appl Math, 1961, 14: 415–426
|
| 17 |
JournéJ-L. Caldeón-Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón. Lecture Notes in Math, Vol 994. Berlin: Springer-Verlag, 1983
|
| 18 |
LiuL, SawanoY, YangD. Morrey-type spaces on Gauss measure spaces and boundedness of singular integrals. J Geom Anal, 2014, 24: 1007–1051
|
| 19 |
LiuL, YangD. BLO spaces associated with the Ornstein-Uhlenbeck operator. Bull Sci Math, 2008, 132: 633–649
|
| 20 |
LiuL, YangD. Boundedness of Littlewood-Paley operators associated with Gauss measures. J Inequal Appl, 2010, 2010(1): 1–41
|
| 21 |
LiuL, YangD. Characterizations of BMO associated with Gauss measures via commutators of local fractional integrals. Israel J Math, 2010, 180: 285–315
|
| 22 |
LiuL, YangD. Pointwise multipliers for Campanato spaces on Gauss measure spaces. Nagoya Math J, 2014, 214: 169–193
|
| 23 |
MauceriG, MedaS. BMO and H1 for the Ornstein-Uhlenbeck operator. J Funct Anal, 2007, 252: 278–313
|
| 24 |
MauceriG, MedaS, SjögrenP. Sharp estimates for the Ornstein-Uhlenbeck operator. Ann Sc Norm Super Pisa Cl Sci (5), 2004, 3: 447–480
|
| 25 |
ShiX, TorchinskyA. Local sharp maximal functions in spaces of homogeneous type. Sci Sinica Ser A, 1987, 30: 473–480
|
| 26 |
SjögrenP. On the maximal function for the Mehler kernel. In: Harmonic Analysis (Cortona, 1982). Lecture Notes in Math, Vol 992. Berlin: Springer, 1983, 73–82
|
| 27 |
StrömbergJ O. Bounded mean oscillation with Orlicz norms and duality of Hardy spaces. Indiana Univ Math J, 1979, 28: 511–544
|
| 28 |
TolsaX. BMO, H1 and Calderón-Zygmund operators for non doubling measures. Math Ann, 2001, 319: 89–149
|
/
| 〈 |
|
〉 |