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Regularity of Local Bilinear Maximal Operator

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Abstract

In this paper, we introduce and investigate Sobolev regularity properties of the local bilinear maximal operator and its fractional variant. Some new bounds for the derivatives of the above maximal functions are established. These estimates can be used to obtain boundedness and continuity for these operators in Sobolev spaces as well as the bounds of these operators on the Sobolev spaces with zero boundary values.

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Authors and Affiliations

  1. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Feng Liu

  2. Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Shifen Wang & Qingying Xue

Authors
  1. Feng Liu
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  2. Shifen Wang
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  3. Qingying Xue
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Correspondence to Qingying Xue.

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The first author was partly supported by the NNSF of China (No. 11701333). The third author was supported partly by NSFC (No. 11871101), 111 Project and the National Key Research and Development Program of China (Grant No. 2020YFA0712900).

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Liu, F., Wang, S. & Xue, Q. Regularity of Local Bilinear Maximal Operator. Results Math 76, 211 (2021). https://doi.org/10.1007/s00025-021-01522-2

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