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Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

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Języki publikacji
EN
Abstrakty
EN
In this article, we study the generalized parabolic parametric Marcinkiewicz integral operators M(r)Ω,h,Φ,λ related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.
Wydawca
Rocznik
Strony
44--57
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
  • Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
  • Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
Bibliografia
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  • [5] A. Al-Salman, H. Al-Qassem, L. Cheng, and Y. Pan, Lp bounds for the function of Marcinkiewicz, Math. Res. Lett. 9(2002), 697-700.
  • [6] H. Al-Qassem and A. Al-Salman, A note on Marcinkiewicz integral operators, J. Math. Anal. Appl. 282 (2003), no. 2, 698-710.
  • [7] L. Hörmander, Estimates for translation invariant operators in Lp space, Acta Math. 104 (1960), 93 -139.
  • [8] H. Al-Qassem and Y. Pan, Lp estimates for singular integrals with kernels belonging to certain block spaces, Rev. Mat. Iberoam. 18 (2002), no. 3, 701-730.
  • [9] H. Al-Qassem and Y. Pan, On certain estimates for Marcinkiewicz integrals and extrapolation, Collect. Math. 60 (2009), no. 2, 123-145.
  • [10] M. Ali and A. Al-Senjlawi, Boundedness of Marcinkiewicz integrals on product spaces and extrapolation, Int. J. Pure Appl. Math. 97 (2014), no. 1, 49-66.
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  • [12] Y. Ding, On Marcinkiewicz integral, Proceedings of the Conference Singular Integrals and Related Topics III, Osaka, Japan, 2001.
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  • [14] Y. Ding, S. Lu, and K. Yabuta, A problem on rough parametric Marcinkiewicz functions, J. Aust. Math. Soc. 72(2002), no. 1, 13-21.
  • [15] M. Ali, Lp estimates for Marcinkiewicz integral operators and extrapolation, J. Inequal. Appl. (2014), DOI: 10.1186/1029242X-2014-269
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  • [17] J. Chen, D. Fan, Y. Ying, Singular integral operators on function spaces, J. Math. Anal. Appl. 276 (2002), 691-708.
  • [18] H. Le, Singular integrals with mixed homogeneity in Triebel-Lizorkin spaces, J. Math. Anal. Appl. 345 (2008), 903-916.
  • [19] H. Al-Qassem, L. Cheng, and Y Pan, On generalized Littlewood-Paley functions, Collect. Math. 69 (2018), no. 2, 297-314.
  • [20] H. Al-Qassem, L. Cheng, and Y. Pan, On rough generalized parametric Marcinkiewicz integrals, J. Math. Inequal. 11(2017), no. 3, 763-780.
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  • [22] M. Ali and M. Alquran, Boundedness of generalized parametric Marcinkiewicz integrals associated to surfaces, submitted.
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Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0bf66297-d6c4-4814-9c4d-50b96ae15cdb
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