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Sobolev regularity for a class of local fractional new maximal operators

  • Rui Li and Shuangping Tao EMAIL logo
Published/Copyright: August 3, 2024
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 32 Issue 1

Abstract

This paper is devoted to studying the regularity properties for the new maximal operator M φ and the fractional new maximal operator M φ , β in the local case. Some new pointwise gradient estimates of M φ , Ω and M φ , β , Ω are given. Moreover, the boundedness of M φ , Ω and M φ , β , Ω on Sobolev space is established. As applications, we also obtain the bounds of the above operators on Sobolev space with zero boundary values.

Keywords: Local fractional new maximal operator; regularity; Sobolev boundedness; partial derivative; pointwise gradient inequality
MSC 2020: 46E35; 42B25; 47H99

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12361018

Funding statement: This research is supported by the National Natural Science Foundation of China (Grant No. 12361018).

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Received: 2023-10-19
Revised: 2024-02-25
Accepted: 2024-03-12
Published Online: 2024-08-03
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. A note on higher order Dirac operators in Clifford analysis
  3. Action of higher derivations on semiprime rings
  4. Demicompact linear operator. Essential pseudospectra and perturbation
  5. On the rotations and limit cycles of solutions to the basic system of equations
  6. On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
  7. A class of nontrivial simple examples of a non-D-space
  8. A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
  9. A property of the free Gaussian distribution
  10. The influence of c-subnormality subgroups on the structure of finite groups
  11. Wave propagation on hexagonal lattices
  12. Timelike zero mean curvature surfaces in ℝ1 4
  13. A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
  14. On corrected Simpson-type inequalities via local fractional integrals
  15. Sobolev regularity for a class of local fractional new maximal operators
  16. On the singular directions of a holomorphic mapping in P n(ℂ)
  17. On minimal surfaces in ℍ2 × ℝ space
  18. Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
  19. Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
  20. On generalized derivations in factor rings
  21. Remarks on generalized derivations in factor rings
https://doi.org/10.1515/gmj-2024-2039
Keywords for this article
Local fractional new maximal operator; regularity; Sobolev boundedness; partial derivative; pointwise gradient inequality

Articles in the same Issue

  1. Frontmatter
  2. A note on higher order Dirac operators in Clifford analysis
  3. Action of higher derivations on semiprime rings
  4. Demicompact linear operator. Essential pseudospectra and perturbation
  5. On the rotations and limit cycles of solutions to the basic system of equations
  6. On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
  7. A class of nontrivial simple examples of a non-D-space
  8. A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
  9. A property of the free Gaussian distribution
  10. The influence of c-subnormality subgroups on the structure of finite groups
  11. Wave propagation on hexagonal lattices
  12. Timelike zero mean curvature surfaces in ℝ1 4
  13. A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
  14. On corrected Simpson-type inequalities via local fractional integrals
  15. Sobolev regularity for a class of local fractional new maximal operators
  16. On the singular directions of a holomorphic mapping in P n(ℂ)
  17. On minimal surfaces in ℍ2 × ℝ space
  18. Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
  19. Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
  20. On generalized derivations in factor rings
  21. Remarks on generalized derivations in factor rings
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