Variation Inequalities for One-Sided Singular Integrals and Related Commutators

Feng Liu, Seongtae Jhang, Sung-Kwun Oh and Zunwei Fu
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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

Mathematics, 2019, vol. 7, issue 10, 1-19

Abstract: We establish one-sided weighted endpoint estimates for the ? -variation ( ? > 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 ? -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.

Keywords: ?-variation; one-sided singular integral; commutator; one-sided weighted Morrey space; one-sided weighted Campanato space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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