Boundedness of commutators of rough Hardy operators on grand variable Herz spaces

References

[1] M. Asim, A. Hussain and N. Sarfraz, Weighted variable Morrey–Herz estimates for fractional Hardy operators, J. Inequal. Appl. 2022 (2022), Paper No. 2. Search in Google Scholar

[2] S. Bashir, B. Sultan, A. Hussain, A. Khan and T. Abdeljawad, A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent, AIMS Math. 8 (2023), no. 9, 22178–22191. 10.3934/math.20231130Search in Google Scholar

[3] D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces, Foundations and Harmonic Analysis, Appl. Numer. Harmon. Anal., Birkhäuser, Heidelberg, 2013. 10.1007/978-3-0348-0548-3Search in Google Scholar

[4] Z. Fu, L. Grafakos, S. Lu and F. Zhao, Sharp bounds for m-linear Hardy and Hilbert operators, Houston J. Math. 38 (2012), no. 1, 225–244. Search in Google Scholar

[5] Z.-W. Fu, Z.-G. Liu, S.-Z. Lu and H.-B. Wang, Characterization for commutators of n-dimensional fractional Hardy operators, Sci. China Ser. A 50 (2007), no. 10, 1418–1426. 10.1007/s11425-007-0094-4Search in Google Scholar

[6] A. Hussain, M. Asim, M. Aslam and F. Jarad, Commutators of the fractional Hardy operator on weighted variable Herz–Morrey spaces, J. Funct. Spaces 2021 (2021), Article ID 9705250. 10.1155/2021/9705250Search in Google Scholar

[7] A. Hussain, M. Asim and F. Jarad, Variable λ-central Morrey space estimates for the fractional Hardy operators and commutators, J. Math. 2022 (2022), Article ID 5855068. 10.1186/s13660-021-02739-zSearch in Google Scholar

[8] M. Izuki, Boundedness of vector-valued sublinear operators on Herz–Morrey spaces with variable exponent, Math. Sci. Res. J. 13 (2009), no. 10, 243–253. 10.11650/twjm/1500405453Search in Google Scholar

[9] M. Izuki, Boundedness of commutators on Herz spaces with variable exponent, Rend. Circ. Mat. Palermo (2) 59 (2010), no. 2, 199–213. 10.1007/s12215-010-0015-1Search in Google Scholar

[10] V. Kokilashvili, A. Meskhi, H. Rafeiro and S. Samko, Integral Operators in Non-Standard Function Spaces. Vol. 1: Variable Exponent Lebesgue and Amalgam Spaces, Oper. Theory Adv. Appl. 248, Birkhäuser/Springer, Cham, 2016. 10.1007/978-3-319-21015-5_1Search in Google Scholar

[11] V. Kokilashvili, A. Meskhi, H. Rafeiro and S. Samko, Integral Operators in Non-Standard Function Spaces. Vol. 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces, Oper. Theory Adv. Appl. 249, Birkhäuser/Springer, Cham, 2016. 10.1007/978-3-319-21015-5Search in Google Scholar

[12] H. Nafis, H. Rafeiro and M. A. Zaighum, A note on the boundedness of sublinear operators on grand variable Herz spaces, J. Inequal. Appl. 2020 (2020), Paper No. 1. 10.1186/s13660-019-2265-6Search in Google Scholar

[13] H. Nafis, H. Rafeiro and M. A. Zaighum, Boundedness of the Marcinkiewicz integral on grand variable Herz spaces, J. Math. Inequal. 15 (2021), no. 2, 739–753. 10.7153/jmi-2021-15-52Search in Google Scholar

[14] H. Nafis, H. Rafeiro and M. A. Zaighum, Boundedness of multilinear Calderón–Zygmund operators on grand variable Herz spaces, J. Funct. Spaces 2022 (2022), Article ID 4845507. 10.1155/2022/4845507Search in Google Scholar

[15] S. Samko, Variable exponent Herz spaces, Mediterr. J. Math. 10 (2013), no. 4, 2007–2025. 10.1007/s00009-013-0285-xSearch in Google Scholar

[16] B. Sultan, F. Azmi, M. Sultan, M. Mehmood and N. Mlaiki, Boundedness of Riesz potential operator on grand Herz–Morrey spaces, Axioms 11 (2022), no. 11, Paper No. 583. 10.3390/axioms11110583Search in Google Scholar

[17] B. Sultan, F. M. Azmi, M. Sultan, T. Mahmood, N. Mlaiki and N. Souayah, Boundedness of fractional integrals on grand weighted Herz–Morrey spaces with variable exponent, Fract. Fractional. 6 (2022), no. 11, Paper No. 660. 10.3390/fractalfract6110660Search in Google Scholar

[18] B. Sultan, M. Sultan, M. Mehmood, F. Azmi, M. A. Alghafli and N. Mlaiki, Boundedness of fractional integrals on grand weighted Herz spaces with variable exponent, AIMS Math. 8 (2023), no. 1, 752–764. 10.3934/math.2023036Search in Google Scholar

[19] M. Sultan, B. Sultan, A. Aloqaily and N. Mlaiki, Boundedness of some operators on grand Herz spaces with variable exponent, AIMS Math. 8 (2023), no. 6, 12964–12985. 10.3934/math.2023653Search in Google Scholar

[20] M. Sultan, B. Sultan, A. Khan and T. Abdeljawad, Boundedness of Marcinkiewicz integral operator of variable order in grand Herz–Morrey spaces, AIMS Math. 8 (2023), no. 9, 22338–22353. 10.3934/math.20231139Search in Google Scholar

[21] B. Sultan, M. Sultan and I. Khan, On Sobolev theorem for higher commutators of fractional integrals in grand variable Herz spaces, Commun. Nonlinear Sci. Numer. Simul. 126 (2023), 10.1016/j.cnsns.2023.107464. 10.1016/j.cnsns.2023.107464Search in Google Scholar

[22] H. Wang, Commutators of Marcinkiewicz integrals on Herz spaces with variable exponent, Czechoslovak Math. J. 66(141) (2016), no. 1, 251–269. 10.1007/s10587-016-0254-1Search in Google Scholar

[23] J. Wu, Boundedness for fractional Hardy-type operator on Herz–Morrey spaces with variable exponent, Bull. Korean Math. Soc. 51 (2014), no. 2, 423–435. 10.4134/BKMS.2014.51.2.423Search in Google Scholar