COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

Rui BU; Jiecheng CHEN; Guoen HU

doi:10.1016/S0252-9602(17)30079-6

Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 5: 1373 - 1384

DOI: https://doi.org/10.1016/S0252-9602(17)30079-6

Articles

COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

Rui BU ,
Jiecheng CHEN ,
Guoen HU

Expand

1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China;
2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
3. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China

Received date: 2016-02-21

Revised date: 2016-10-30

Online published: 2017-10-25

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).

Fold

Abstract

Let α ∈ (0,(n-1)/2) and T^α be the Bochner-Riesz operator of order α.In this paper,for n=2 and n ≥ 3,the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO (Rⁿ) function and Tα.

Key words： Bochner-Riesz operator; commutator; compact operator; Fourier transform estimate

Cite this article

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 . DOI: 10.1016/S0252-9602(17)30079-6

References

[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

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article

References