Weighted Endpoint Estimates for Maximal Commutators Associated with the Sections
Weighted Endpoint Estimates for Maximal Commutators Associated with the Sections
摘要
We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation.
We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation.
基金
Supported by National Science Foundationof China (Grant Nos. 10571156 and 10871173)
参考文献16
-
1Caffarelli, L. Gutierrez. C.: Real analysis related to the Monge-Ampere equation. Trans. Amer. Math. Soc., 348, 1075-1092 (1996).
-
2Caffarelli, L., Gutierrez, C.: Singular integrals related to Monge-Ampere equation. In: Wavelet Theory and Harmonic Analysis in Applied Sciences, Buenos Aires, 1995. In: Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 1997, 3-13.
-
3Incognito, A.: Weak-type (1, 1) inequality for the Monge-Ampere equation SIOs. J. Fourier Anal. Appl., T, 41-48 (2001).
-
4Tang, L.: Weighted estimates for singular integral operators and commutators associated with the sections. J. Math. Anal. Appl., 333, 577-590 (2007).
-
5Perez, C.: Endpoint estimates for commutators of singular integral operators. J. Funct. Anal., 128, 163-185 (1995).
-
6Alphonse, A. M.: An end point estimate for maximal commutators. J. Fourier Anal. Appl., 6, 449 456 (2000).
-
7Aimar, H., Forzani, L., Toledano R.: Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampere equation. J. Fourier Anal. Appl., 4, 377-381 (1998).
-
8Gutierrez, C., Huang, Q.: Geometric properties of solutions to the Monge-Ampere equation. Trans. Amer. Math. Soc., 352, 4381- 4396 (2000).
-
9Hu, G., Yang, D., Yang, Do.: Boundedness of maximal singular integral operators on spaces of homogeneous type and its applications. J. Math. Soc. Japan., 59, 323-349 (2007).
-
10Rao, M., Ren, Z.: Theory of Orlicz Spaces, Monogr. Textbooks Pure Appl. Math., Vol. 146, Marcel Dekker, New York, 1991.
-
1Xiaoli CHEN.Some Endpoint Estimates for the Multiplier Operator[J].Journal of Mathematical Research with Applications,2012,32(3):337-345.
-
2Yan LIN.Endpoint Estimates for Calderon-Zygmund Type Operators[J].Acta Mathematica Sinica,English Series,2010,26(3):523-532. 被引量:3
-
3ZHAO FaYou,FU ZunWei,LU ShanZhen.Endpoint estimates for n-dimensional Hardy operators and their commutators[J].Science China Mathematics,2012,55(10):1977-1990. 被引量:21
-
4Yan LIN,Mei XU.Endpoint Estimates for Marcinkiewicz Integrals on Weighted Weak Hardy Spaces[J].Acta Mathematica Sinica,English Series,2015,31(3):430-444. 被引量:3
-
5Xiaoli Chen,Jie Sun,Dongxiang Chen.SOME ENDPOINT ESTIMATES FOR COMMUTATORS OF θ-TYPE CALDERóN-ZYGMUND OPERATORS[J].Analysis in Theory and Applications,2009,25(2):175-181. 被引量:2
-
6LU Shanzhen and MENG Yan(Department of Mathematics, Beijing Normal University,Beijing 100875, China).Endpoint estimates for a class of multilinear oscillatory singular integral operators[J].Progress in Natural Science:Materials International,2002,12(11):813-819.
-
7QIN XI-MEI XIE RU-LONG.Weighted Endpoint Estimates for Multilinear θ-type Calderón-Zygmund Operator[J].Communications in Mathematical Research,2009,25(5):461-471.
-
8杨杰,王宇钊,陈文艺.ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS[J].Acta Mathematica Scientia,2014,34(2):387-393. 被引量:2
-
9江寅生.ENDPOINT ESTIMATES FOR FRACTIONAL INTEGRAL ASSOCIATED TO SCHRDINGER OPERATORS ON THE HEISENBERG GROUPS[J].Acta Mathematica Scientia,2011,31(3):993-1000. 被引量:2
-
10Xudong Nie,Shimo Wang,Dunyan Yan.Endpoint Estimates for Hardy Operator's Conjugate Operator with Power Weight on n-Dimensional Space[J].Analysis in Theory and Applications,2013,29(3):267-274. 被引量:1