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Variation Inequalities for One-Sided Singular Integrals and Related Commutators

Author

Listed:
  • Feng Liu

    (College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Seongtae Jhang

    (Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do 445-743, Korea)

  • Sung-Kwun Oh

    (Department of Electrical Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do 445-743, Korea)

  • Zunwei Fu

    (Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do 445-743, Korea
    School of Mathematical Sciences, Qufu Normal University, Qufu 273000, China)

Abstract

We establish one-sided weighted endpoint estimates for the ϱ -variation ( ϱ > 2 ) operators of one-sided singular integrals under certain priori assumption by applying one-sided Calderón–Zygmund argument. Using one-sided sharp maximal estimates, we further prove that the ϱ -variation operators of related commutators are bounded on one-sided weighted Lebesgue and Morrey spaces. In addition, we also show that these operators are bounded from one-sided weighted Morrey spaces to one-sided weighted Campanato spaces. As applications, we obtain some results for the λ -jump operators and the numbers of up-crossings. Our main results represent one-sided extensions of many previously known ones.

Suggested Citation

  • Feng Liu & Seongtae Jhang & Sung-Kwun Oh & Zunwei Fu, 2019. "Variation Inequalities for One-Sided Singular Integrals and Related Commutators," Mathematics, MDPI, vol. 7(10), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:876-:d:269315
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    References listed on IDEAS

    as
    1. Shaoguang Shi & Zunwei Fu, 2013. "Estimates of Some Operators on One-Sided Weighted Morrey Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
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    Cited by:

    1. Yu Yan & Yiming Wang & Yiming Lei, 2022. "A p Weights in Directionally ( γ , m ) Limited Space and Applications," Mathematics, MDPI, vol. 10(19), pages 1-13, September.

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