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## COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS ON NON-HOMOGENEOUS METRIC MEASURE SPACES

Citations: | 1 - 1 self |

### Citations

94 |
On commutators of singular integrals and bilinear singular integrals
- Coifman, Meyer
(Show Context)
Citation Context ...utators of Calderón-Zygmund operators on Orlicz spaces on non-homogeneous spaces. On the other hand, the theory on multilinear singular integral operators has been considered by some researchers. In =-=[3]-=-, Coifman and Meyers firstly established the theory of bilinear Calderón-Zygmund operators. Later, Gorafakos and Torres [6-7] established the boundedness of multilinear singular integral on the produ... |

93 | Multilinear Calderón–Zygmund theory. - Grafakos, Torres - 2002 |

90 | The Tb-theorem on non-homogeneous spaces, - Nazarov, Treil, et al. - 2003 |

76 | Painleve’s problem and the semiadditivity of analytic capacity,”
- Tolsa
- 2003
(Show Context)
Citation Context ...gh brings rapid development in harmonic analysis (see [2,5,8-9,17-22]). And the analysis on non-doubling measures has important applications in solving the long-standing open Painlevé’s problem (see =-=[18]-=-). However, as stated by Hytönen in [11], the measure satisfying (1) does not include the doubling measure as special cases. To solve this problem, a kind of metric measure space (X, d, µ), which is ... |

55 |
Calderón-Zygmund operators for non doubling measures
- Tolsa, “BMO
- 2001
(Show Context)
Citation Context ...∈ L1loc(µ) with ∫ X f(x)dµ(x) = 0 if ||µ|| <∞. For 1 < p <∞ and 0 < δ < 1, if inf(1, Nδf) ∈ L p(µ), then there exists a constant C > 0 such that (2.6) ||Nδ(f)||Lp(µ) ≤ C||M ♯ δ (f)||Lp(µ). Lemma 2.2. =-=[4,19]-=- Let 1 ≤ p < ∞ and 1 < ρ < ∞. Then b ∈ RBMO(µ) if and only if for any ball B ⊂ X, (2.7) { 1 µ(ρB) ∫ B |bB −mB̃(b)| pdµ(x) }1/p ≤ C||b||∗, and for any two doubling balls B ⊂ Q, (2.8) |mB(b)−mQ(b)| ≤ CK... |

40 | Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces,” - Hytonen, Martikainen - 2012 |

20 | A framework for non-homogeneous analysis on metric spaces, and the RBMO
- Hytonen
- 2010
(Show Context)
Citation Context ...nalysis (see [2,5,8-9,17-22]). And the analysis on non-doubling measures has important applications in solving the long-standing open Painlevé’s problem (see [18]). However, as stated by Hytönen in =-=[11]-=-, the measure satisfying (1) does not include the doubling measure as special cases. To solve this problem, a kind of metric measure space (X, d, µ), which is called non-homogeneous metric measures sp... |

19 | Two-weight norm inequalities for maximal operators and fractional integrals on non-homogeneous spaces
- Garcı́a-Cuerva, Marı́a-Martell
- 2001
(Show Context)
Citation Context ...d r > 0, there exist a constant C0 > 0 and k ∈ (0, n] such that, (1.1) µ(B(x, r)) ≤ C0r k, where B(x, r) = {y ∈ Rn : |y − x| < r}. This breakthrough brings rapid development in harmonic analysis (see =-=[2,5,8-9,17-22]-=-). And the analysis on non-doubling measures has important applications in solving the long-standing open Painlevé’s problem (see [18]). However, as stated by Hytönen in [11], the measure satisfying... |

19 | On multilinear singular integrals of Calderón– Zygmund type, Publ - Grafakos, Torres |

14 | A note on commutators of fractional integrals with RBMO μ functions - Chen, Sawyer - 2002 |

12 |
TheHardy spaceH1 on nonhomogeneous metric spaces,”
- Yang
- 2012
(Show Context)
Citation Context ...owth measures as special cases. From then on, some results paralled to homogeneous spaces and non-doubling measures space are obtained (see [1,5,11-16] and the references therein). Hytönen et al. in =-=[14]-=- and Bui and Duong in [1] independently introduced the atomic Hardy spaceH1(µ) and proved that the dual space 0* Corresponding author 1991 Mathematics Subject Classification. 42B20; 42B25. Key words a... |

10 | Multilinear commutators of singular integrals with non doubling measures - Hu, Meng, et al. - 2005 |

8 | Spaces of type BLO on non-homogeneous metric measure,” - Lin, Yang - 2011 |

7 | New atomic characterization of H1 space with nondoubling measures and its applications - Hu, Meng, et al. |

6 |
Boundedness of Calderón-Zygmund operators on nonhomogeneous metric measure spaces: equivalent characterizations
- Yang, Yang
(Show Context)
Citation Context ...ón-Zygmund operator and commutators of Calderón-Zygmund operators and RBMO functions are bounded in Lp(µ) for 1 < p < ∞. Recently, some equivalent characterizations are established by Liu et al. in =-=[16]-=- for the boundedness of Carderon-Zygmund operators on Lp(µ) for 1 < p < ∞. In [4], Fu et al. established boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces on non-h... |

6 | Boundedness of multilinear singular integrals for non-doubling measures - Xu - 2007 |

5 |
Weighted norm inequalities for multilinear Calderon-Zygmund operators on nonhomogeneous metric measure spaces,”
- Hu, Meng, et al.
- 2014
(Show Context)
Citation Context ...ing measures spaces (Rn, µ) were established by Xu in [21-22]. Weighted norm inequalities for multilinear Calderón-Zygmund operators on non-homogeneous metric measure spaces were also constructed in =-=[10]-=-. In the setting of non-homogeneous metric measure spaces, it is natural to ask whether commutators of multilinear singular integral operators is also bounded in m-multiple Lebesgue spaces. This paper... |

4 |
Boundedness of multilinear commutators of Calderon-Zygmund operators onOrlicz spaces over non-homogeneous spaces,”
- Fu, Yang, et al.
- 2012
(Show Context)
Citation Context ...ions are bounded in Lp(µ) for 1 < p < ∞. Recently, some equivalent characterizations are established by Liu et al. in [16] for the boundedness of Carderon-Zygmund operators on Lp(µ) for 1 < p < ∞. In =-=[4]-=-, Fu et al. established boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces on non-homogeneous spaces. On the other hand, the theory on multilinear singular integral... |

4 | Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures - Xu - 2007 |

3 | Θ-type Calderon-Zygmund operators with non-doubling measures,” - Xie, Shu - 2013 |

2 |
spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces
- Bui, Duong, et al.
(Show Context)
Citation Context ... the homogeneous spaces and metric spaces with polynomial growth measures as special cases. From then on, some results paralled to homogeneous spaces and non-doubling measures space are obtained (see =-=[1,5,11-16]-=- and the references therein). Hytönen et al. in [14] and Bui and Duong in [1] independently introduced the atomic Hardy spaceH1(µ) and proved that the dual space 0* Corresponding author 1991 Mathemat... |