Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1373-1384.doi: 10.1016/S0252-9602(17)30079-6
• Articles • Previous Articles Next Articles
Rui BU1, Jiecheng CHEN2, Guoen HU3
Received:2016-02-21
Revised:2016-10-30
Online:2017-10-25
Published:2017-10-25
Contact:
Guoen HU,E-mail:guoenxx@163.com
E-mail:guoenxx@163.com
Supported by:The research of Bu was supported by the NNSF of China (11571306), and the research of Chen was supported by the NNSF of China (11271330 and 11671363), and the research of Hu was supported by the NNSF of China (11371370).
Rui BU, Jiecheng CHEN, Guoen HU. COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR[J].Acta mathematica scientia,Series B, 2017, 37(5): 1373-1384.
| [1] Bochner S. Summation of multiple Fourier series by spherical means. Trans Amer Math Soc, 1936, 40:175-207 [2] Herz C. On the mean inversion of Fourier and Hankel transforms. Proc Nat Acad Sci, USA, 1954, 40:996-999 [3] Stein E M. Interpolation of linear operators. Trans Amer Math Soc, 1956, 83:482-492 [4] Carleson L, Sjölin P. Oscillatory integrals and a multiplier problem for the disc. Studia Math, 1972, 44:287-299 [5] Fefferman C. A note on spherical summation multipliers. Israeli J Math, 1973, 15:44-52 [6] Grafakos L. Modern Fourier Analysis. New York:Springer, 2008 [7] Hu G, Lu S. The commutator of the Bochner-Riesz operator. Tohoku Math J, 1996, 48:259-266 [8] Hu G, Lu S. A weighted L2 estimates for the commutator of the Bochner-Riesz operator. Proc Amer Math Soc, 1997, 125:2867-2873 [9] Kim Y. Weighted norm inequalities of the maximal commutator of quasiradial Bochner-Riesz operators. Acta Math Sin, English Ser, 2013, 29:1743-1756 [10] Liu Z, Lu G, Lu S. Continuity properties for the maximal operator associated with the commutator of the Bochner-Riesz operator. Publ Mat, 2003, 47:45-70 [11] Uchiyama A. On the compactness of operators of Hankel type. Tohoku Math J, 1978, 30:163-171 [12] Bourdaud G, Lanze de Cristoforis M, Sickel W. Functional calculus on BMO and related spaces. J Funct Anal, 2002, 189:515-538 [13] Coifman R, Weiss G. Extension of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83:569-645 [14] Chen J, Hu G. Compact commutators of rough singular integral operators. Canad Math Bull, 2015, 58:19-29 [15] Morrey C. On the solution of quasi-linear elliptic partial differential equation. Trans Amer Math Soc, 1938, 43:126-166 [16] Ruiz A, Vega L. Unique continuation for Schrödinger operators with potential in Morrey space. Publ Mat, 1991, 35:291-298 [17] Adams D R, Xiao J. Morrey spaces in harmonic analysis. Ark Mat, 2012, 50(2):201-230 [18] Adams D R, Xiao J. Regularity of Morrey commutators. Trans Amer Math Soc, 2012, 364(9):4801-4818 [19] Lin H, Yang D. Pointwise multipliers for locasized Morrey-Campanato spaces on RD-spaces. Acta Math Sci, 2014, 34B(6):1677-1694 [20] Yang Q. Characterization of multiplier spaces with daubechies wavelets. Acta Math Sci, 2012, 32B(6):2315-2321 [21] Chen Y, Ding Y, Wang X. Compactness of commutators for singular integrals on Morrey spaces. Canad J Math, 2012, 64:257-281 [22] Yosida K. Function Analysis. Berlin:Springer-Verlag, 1995 [23] Stein E M, Weiss G. Interpolation of operators with changes of measures. Trans Amer Math Soc, 1958, 87:159-172 [24] Muckenhoupt B, Wheeden R. Weighted norm inequalities for fractional integrals. Trans Amer Math Soc, 1974, 192:261-274 |
| [1] | Afif BEN AMAR. THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS [J]. Acta mathematica scientia,Series B, 2014, 34(2): 263-273. |
| [2] | YANG Jie, WANG Yu-Zhao, CHEN Wen-Yi. ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS [J]. Acta mathematica scientia,Series B, 2014, 34(2): 387-393. |
| [3] | GUO Chun-Xiao, ZHANG Jing-Jun, GUO Bo-Ling. EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION [J]. Acta mathematica scientia,Series B, 2013, 33(4): 883-900. |
| [4] | Metin BASARIR, Emrah Evren KARA. ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS [J]. Acta mathematica scientia,Series B, 2013, 33(3): 797-813. |
| [5] | LI Peng-Tao, PENG Li-Zhong. Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP [J]. Acta mathematica scientia,Series B, 2012, 32(2): 568-578. |
| [6] | YANG Qi-Xiang. Lp CONTINUITY OF HÖRMANDER SYMBOL OPERATORS OpSm0,0 AND NUMERICAL ALGORITHM [J]. Acta mathematica scientia,Series B, 2011, 31(4): 1517-1534. |
| [7] | HU Guo-En, ZHU Yue-Ping. WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS [J]. Acta mathematica scientia,Series B, 2011, 31(3): 749-764. |
| [8] | LIU Yong-Min, YU Yan-Yan. ON COMPACTNESS FOR ITERATED COMMUTATORS [J]. Acta mathematica scientia,Series B, 2011, 31(2): 491-500. |
| [9] | XIA Xia, LU Shan-Zhan. COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR A CLASS OF RADIAL FUNCTIONS [J]. Acta mathematica scientia,Series B, 2011, 31(2): 477-482. |
| [10] | Mo Huixia; Lu Shanzhen. BOUNDEDNESS OF GENERALIZED HIGHER COMMUTATORS OF MARCINKIEWICZ INTEGRALS [J]. Acta mathematica scientia,Series B, 2007, 27(4): 852-866. |
| [11] | Zhou Weijun; Ma Bolin; Xu Jingshi. THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS ON WEIGHTED SPACES#br# AND HERZ-TYPE SPACES [J]. Acta mathematica scientia,Series B, 2007, 27(2): 361-372. |
| [12] | Hu Guoen; Meng Yan; Yang Dachun. ENDPOINT ESTIMATE FOR MAXIMAL COMMUTATORS WITH NON-DOUBLING MEASUES [J]. Acta mathematica scientia,Series B, 2006, 26(2): 271-280. |
| [13] | HU Guo-En. ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS [J]. Acta mathematica scientia,Series B, 2005, 25(3): 545-554. |
| [14] | DENG Dong-Gao, YA Li-Xin. COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS [J]. Acta mathematica scientia,Series B, 2005, 25(1): 137-144. |
| [15] | Liu-Li-Fang, CAO Guang-Fu, WANG Xiao-Feng. COMPOSITION OPERATORS ON HARDY-ORLICZ SPACES [J]. Acta mathematica scientia,Series B, 2005, 25(1): 105-111. |
| Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
|
Full text 23
|
|
|||||||||||||||||||||||||||||||||||||||||||||
|
Abstract 122
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
| Shared | ||||||||||||||||||||||||||||||||||||||||||||||
| Discussed | ||||||||||||||||||||||||||||||||||||||||||||||
|