Research article Special Issues

Boundedness of sublinear operators on weighted grand Herz-Morrey spaces

  • Received: 29 December 2022 Revised: 02 May 2023 Accepted: 06 May 2023 Published: 19 May 2023
  • MSC : 42B25, 42B35, 46E30

  • In this paper, we introduce weighted grand Herz-Morrey type spaces and prove the boundedness of sublinear operators and their multilinear commutators on these spaces. The results are still new even in the unweighted setting.

    Citation: Wanjing Zhang, Suixin He, Jing Zhang. Boundedness of sublinear operators on weighted grand Herz-Morrey spaces[J]. AIMS Mathematics, 2023, 8(8): 17381-17401. doi: 10.3934/math.2023888

    Related Papers:

  • In this paper, we introduce weighted grand Herz-Morrey type spaces and prove the boundedness of sublinear operators and their multilinear commutators on these spaces. The results are still new even in the unweighted setting.



    加载中


    [1] O. Kov$\rm \acute{a}\rm \breve{c}$ik, J. R$\rm \acute{a}$kosník, On spaces $L^{p(x)}$ and $W^{k, p(x)}$, Czechoslovak Math. J., 41 (1991), 592–618. http://dx.doi.org/10.21136/CMJ.1991.102493 doi: 10.21136/CMJ.1991.102493
    [2] P. Gurka, P. Harjulehto, A. Nekvinda, Bessel potential spaces with variable exponent, Math. Inequal. Appl., 10 (2007), 661–676. http://dx.doi.org/10.7153/mia-10-61 doi: 10.7153/mia-10-61
    [3] A. Almeida, P. H$\rm\ddot{a}$st$\rm \ddot{o}, $ Besov spaces with variable smoothness and integrability, J. Funct. Anal., 258 (2010), 1628–1655. http://dx.doi.org/10.1016/j.jfa.2009.09.012
    [4] D. Drihem, Atomic decomposition of Besov spaces with variable smoothness and integrability, J. Math. Anal. Appl., 389 (2012), 15–31. http://dx.doi.org/10.1016/j.jmaa.2011.11.035 doi: 10.1016/j.jmaa.2011.11.035
    [5] J. S. Xu, Variable Besov spaces and Triebel-Lizorkin spaces, Ann. Acad. Sci. Fenn. Math., 33 (2008), 511–522.
    [6] X. L. Fan, Variable exponent Morrey and Campanato spaces, Nonlinear Anal., 72 (2010), 4148–4161. http://dx.doi.org/10.1016/j.na.2010.01.047 doi: 10.1016/j.na.2010.01.047
    [7] H. Rafeiro, S. Samko, Variable exponent Campanato spaces, J. Math. Sci., 172 (2011), 143–164. http://dx.doi.org/10.1007/S10958-010-0189-2 doi: 10.1007/S10958-010-0189-2
    [8] M. Izuki, Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization, Anal. Math., 36 (2010), 33–50. http://dx.doi.org/10.1007/S10476-010-0102-8 doi: 10.1007/S10476-010-0102-8
    [9] M. Izuki, Boundedness of commutators on Herz spaces with variable exponent, Rend. Circ. Mat. Palermo, 59 (2010), 199–213. http://dx.doi.org/10.1007/S12215-010-0015-1 doi: 10.1007/S12215-010-0015-1
    [10] M. Izuki, Boundedness of vector-valued sublinear operators on Herz-Morrey spaces with variable exponent, Math. Sci. Res. J., 13 (2009), 243–253.
    [11] S. R. Wang, J. S. Xu, Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents, Open Math., 19 (2021), 412–426. http://dx.doi.org/10.1515/math-2021-0024 doi: 10.1515/math-2021-0024
    [12] B. Sultan, M. Sultan, M. Mehmood, F. Azmi, M. A. Alghafli, N. Mlaiki, Boundedness of fractional integrals on grand weighted Herz spaces with variable exponent, AIMS Math., 8 (2023), 752–764. http://dx.doi.org/10.3934/math.2023036 doi: 10.3934/math.2023036
    [13] D. Cruz-Uribe, A. Fiorenza, Variable Lebesgue spaces: foundations and harmonic analysis, Basel: Bikh{$\rm \ddot{a}$}user, 2013.
    [14] L. Diening, P. Harjulehto, P. Hästö, M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Berlin: Springer, 2011. https://doi.org/10.1007/978-3-642-18363-8
    [15] D. Cruz-Uribe, A. Fiorenza, C. J. Neugebauer, The maximal function on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn. Math., 28 (2003), 223–238.
    [16] L. Diening, Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$, Math. Inequal. Appl., 7 (2004), 245–253. http://dx.doi.org/10.7153/mia-07-27 doi: 10.7153/mia-07-27
    [17] D. Cruz-Uribe, A. Fiorenza, C. J. Neugebauer, Weighted norm inequalities for the maximal operator on variable Lebesgue spaces, J. Math. Anal. Appl., 394 (2012), 744–760. http://dx.doi.org/10.1016/j.jmaa.2012.04.044 doi: 10.1016/j.jmaa.2012.04.044
    [18] M. Izuki, T. Noi, Boundedness of fractional integrals on weighted Herz spaces with variable exponent, J. Inequal. Appl., 2016 (2016), 1–15. http://dx.doi.org/10.1186/S13660-016-1142-9 doi: 10.1186/S13660-016-1142-9
    [19] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton: Princeton University Press, 1993.
    [20] L. W. Wang, L. S. Shu, Multilinear commutators of singular integral operators in variable exponent Herz-type spaces, Bull. Malays. Math. Sci. Soc., 42 (2019), 1413–1432. http://dx.doi.org/10.1007/S40840-017-0554-0 doi: 10.1007/S40840-017-0554-0
    [21] H. Rafeiro, S. Samko, S. Umarkhadzhiev, Grand Lebesgue sequence spaces, Georgian Math. J., 25 (2018), 291–302. http://dx.doi.org/10.1515/gmj-2018-0017 doi: 10.1515/gmj-2018-0017
    [22] X. Yu, Z. G. Liu, Weighted grand Herz-type spaces and its applications, J. Funct. Spaces, 2022 (2022), 1–12. http://dx.doi.org/10.1155/2022/1369159 doi: 10.1155/2022/1369159
    [23] A. Almeida, D. Drihem, Maximal, potential and singular type operators on Herz spaces with variable exponents, J. Math. Anal. Appl., 394 (2012), 781–795. http://dx.doi.org/10.1016/j.jmaa.2012.04.043 doi: 10.1016/j.jmaa.2012.04.043
    [24] C. Pérez, R. Trujillo-Goneález, Sharp weighted estimates for multilinear commutators, J. Lond. Math. Soc., 65 (2002), 672–692. http://dx.doi.org/10.1112/S0024610702003174 doi: 10.1112/S0024610702003174
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1506) PDF downloads(133) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog