Commutator of Riesz potential in <i>p</i>-adic generalized Morrey spaces

doi:10.1007/s11464-018-0696-x

Front. Math. China

2018, Vol. 13

Issue (3) : 633-645 https://doi.org/10.1007/s11464-018-0696-x

RESEARCH ARTICLE

Commutator of Riesz potential in p-adic generalized Morrey spaces

Huixia MO(

), Xiaojuan WANG, Ruiqing MA

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Download: PDF(166 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Suppose that $I p α$ is the p-adic Riesz potential. In this paper, we established the boundedness of $I p α$ on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential $I p α$ and p-adic generalized Campanato functions.

Keywords p-Adic field p-adic Riesz potential commutator p-adic generalized Morrey function p-adic generalized Campanato function

Corresponding Author(s): Huixia MO

Issue Date: 11 June 2018

Cite this article:

Huixia MO,Xiaojuan WANG,Ruiqing MA. Commutator of Riesz potential in p-adic generalized Morrey spaces[J]. Front. Math. China, 2018, 13(3): 633-645.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0696-x
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I3/633

1	Campanato S. Proprietà di Hölderianità di alcune classi di funzioni. Ann Scuola Norm Sup Pisa, 1963, 17(1-2): 175–188
2	Chuong N M. Harmonic, Wavelet and p-Adic Analysis. Singapore: World Scientific, 2007 https://doi.org/10.1142/6373
3	Haran S. Riesz potentials and explicit sums in arithmetic. Invent Math, 1990, 101(1): 697–703 https://doi.org/10.1007/BF01231521
4	Haran S. Analytic potential theory over the p-adics. Ann Inst Fourier, 1993, 43(4): 905–944 https://doi.org/10.5802/aif.1361
5	Kim Y C. A simple proof of the p-adic version of the Sobolev embedding theorem. Commun Korean Math Soc, 2010, 25(1): 27–36 https://doi.org/10.4134/CKMS.2010.25.1.027
6	Morrey C. On the solutions of quasi-linear elliptic partial differential equations. Trans Amer Math Soc, 1938, 43(1): 126–166 https://doi.org/10.1090/S0002-9947-1938-1501936-8
7	Nakai E. Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math Nachr, 1994, 166(1): 95–103 https://doi.org/10.1002/mana.19941660108
8	Peetre J. On the theory of Lp,λspaces. J Funct Anal, 1969, 4(1): 71–87 https://doi.org/10.1016/0022-1236(69)90022-6
9	Robert A M. A Course in p-Adic Analysis. Berlin: Springer Science & Business Media, 2013
10	Schikhof W H. Ultrametric Calculus: An Introduction to p-adic Analysis. Cambridge: Cambridge Univ Press, 2007
11	Taibleson M H. Fourier Analysis on Local Fields. Princeton: Princeton Univ Press, 2015
12	Vladimirov V S, Volovich I V, Zelenov E I. p-Adic Analysis and Mathematical Physics. Singapore: World Scientific, 1994
13	Volosivets S S. Generalized fractional integrals in p-adic Morrey and Herz spaces. p-Adic Numbers Ultrametric Anal Appl, 2017, 9(1): 53–61
14	Wu Q Y, Fu Z W. Hardy-Littlewood-Sobolev inequalities on p-adic central Morrey spaces. J Funct Spaces Appl, 2015, 2015: 419532
15	Wu Q Y, Fu Z W. Weighted p-adic Hardy operators and their commutators on p-adic central Morrey spaces. Bull Malays Math Sci Soc, 2017, 40(2): 635–654 https://doi.org/10.1007/s40840-017-0444-5
16	Wu Q Y, Mi L, Fu Z W. Boundedness of p-adic Hardy operators and their commutators on p-adic central Morrey and BMO spaces. J Funct Spaces Appl, 2013, 2013: 359193

[1]	Rui BU, Zunwei FU, Yandan ZHANG. Weighted estimates for bilinear square functions with non-smooth kernels and commutators[J]. Front. Math. China, 2020, 15(1): 1-20.
[2]	Yanping CHEN, Liwei WANG. L²( $ℝ n$ ) boundedness for Calderón commutator with rough variable kernel[J]. Front. Math. China, 2018, 13(5): 1013-1031.
[3]	Nguyen Minh CHUONG, Nguyen Thi HONG, Ha Duy HUNG. Bounds of weighted multilinear Hardy-Cesàro operators in p-adic functional spaces[J]. Front. Math. China, 2018, 13(1): 1-24.
[4]	Wei WANG, Jingshi XU. Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces[J]. Front. Math. China, 2017, 12(5): 1235-1246.
[5]	Dongxiang CHEN, Shanzhen LU, Suzhen MAO. Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals[J]. Front. Math. China, 2017, 12(3): 531-558.
[6]	Jing ZHANG,Huoxiong WU. Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces[J]. Front. Math. China, 2016, 11(2): 423-447.
[7]	Wenjuan LI,Qingying XUE. Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces[J]. Front. Math. China, 2014, 9(6): 1325-1347.
[8]	Fayou ZHAO, Shanzhen LU. A characterization of λ-central BMO space[J]. Front Math Chin, 2013, 8(1): 229-238.
[9]	Shikun OU. Bijective maps on standard Borel subgroup of symplectic group preserving commutators[J]. Front Math Chin, 2012, 7(3): 497-512.
[10]	Shanzhen LU. Some results and problems on commutators[J]. Front Math Chin, 2011, 6(5): 821-833.
[11]	Shaoguang SHI, Zunwei FU, Shanzhen LU. Weighted estimates for commutators of one-sided oscillatory integral operators[J]. Front Math Chin, 2011, 6(3): 507-516.
[12]	Shuli GONG, Bolin MA. Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions[J]. Front Math Chin, 2011, 6(3): 427-447.
[13]	Zunwei FU, Shanzhen LU, . Weighted Hardy operators and commutators on Morrey spaces[J]. Front. Math. China, 2010, 5(3): 531-539.
[14]	LU Shanzhen. Marcinkiewicz integral with rough kernels[J]. Front. Math. China, 2008, 3(1): 1-14.
[15]	CHEN Ping, LUO Shunlong. Direct approach to quantum extensions of Fisher information[J]. Front. Math. China, 2007, 2(3): 359-381.

Viewed

Full text

Abstract

Cited

Shared

Discussed