|Table of Contents|

 Weighted Morrey estimates for commutators of fractional integral on homogeneous groups(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2016年03期
Page:
333-339
Research Field:
Publishing date:

Info

Title:
 Weighted Morrey estimates for commutators of fractional integral on homogeneous groups
Author(s):
 HOU Yuexia
 Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, China
Keywords:
 fractional integra BMO function commutator homogeneous group weighted Morrey space
PACS:
O 178
DOI:
10.13338/j.issn.1006-8341.2016.03.010
Abstract:
In the framwork of homogeneous groups, the boundednesses of commutators of fractional integral with BMO functions in weighted Morrey space are studied. Weighted Morrey estimates for commutators of fractional integral on homogeneous groups can be deduced by applying Hölder’s inequality, John-Nirenberg lemma and properties of weighted functions.The results generalize the related result in Euclidean spaces.

References:

 [1] SOBOLEV S L.On a theorem in functional analysis[J].Mat Sbornik,1938,4:471-497.
[2] ZYGMUND P A.On a theorem of Marcinkiewicz concerning interpolation of operations[J].Jour de Math,1956,35(9):223-248.
[3] CHANILLO S.A note on commutators[J].Indiana Univ Math J,1982,31(1):7-16.
[4] STEIN E M.Singular integrals and differentiability properties of functions[M].New Jersey:Princeton Univ Press,1970:116-165.
[5] MUCKENHOUPT B,WHEEDEN R.Weighted norm inequalities for fractional integral[J].Trans Amer Math Soc,1974,192:261-274.
[6] SEGOVIA C,TORREA J.Weighted inequalities for commutators of fractional and singular integrals[J].Publ Mat,1991,35(1):209-235.
[7] DUONG X T,YAN L X.On commutators of fractional integrals[J].P Am Math Soc,2004,132(12):3549-3557.
[8] BERNARDIS A,HARTZSTEIN S,PRADOLINI G.Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type[J].J Math Anal Appl,2006,322(2):825-846.
[9] KOMORI Y,SHIRAI S.Weighted Morrey spaces and a singular integral operator[J].Math Nachr,2009,282(2):219-231.
[10] PEETRE J.On the theory of <i>L<sup>p,λ</sup></i> space[J].J Funct Anal,1969,4(1):71-87.
[11] FOLLAND G B,STEIN E M.Estimates for the <i>^-b</i> complex and analysis on the Heisenberg group[J].Comm Pure Appl Math,1974,27(4):429-522.
[12] BRAMANTI M,BRANDOLINI L.<i>L<sup>p</sup></i> estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogeneous groups[J].Rend Sem Mat Univ Pol Torino,2000,58(4):389-433.
[13] MUCKENHOUPT B.Weighted norm inequalities for the Hardy maximal function[J].Trans Amer Math Soc,1972,165:207-226.
[14] GRAFAKOS L.Modern fourier analysis[M].New York:Springer,2009:279-338.
[15] JOHN F,NIRENBERG L.On functions of bounded mean oscillation[J].Comn Pure Appl Math,1961,14(3):415-426.
[16] HOU Y,NIU P.Weighted Sobolev-Morrey estimates for hypoelliptic operators with drift on homogeneous groups[J].J Math Anal Appl,2015,428(2):1319-1338.
[17] BERNARDIS A,HARTZSTEIN S,PRADOLINI G.Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type[J].J Math Anal Appl,2006,322(2):825-846.
[18] BRAMANTI M,CERUTTI M.Commutators of singular integrals on homogeneous spaces[J].Bollettino Della Unione Matematica Italiana B,1996,10(4):843-884.

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Last Update: 2016-10-08