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The rate of convergence on fractional power dissipative operator on compact manifolds

  • Yali Pan , Dashan Fan and Junyan Zhao EMAIL logo
Published/Copyright: August 23, 2021
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 24 Issue 4

Abstract

On a compact connected manifold M , we concern the fractional power dissipative operator e−tLα , and obtain the almost-everywhere convergence rate (as t → 0+) of e−tLαf when f is in some Sobolev type Hardy spaces. The main result is a non-trivial extension of a recent result on ℝn by Cao and Wang in 2.

MSC 2010: Primary 41A17; Secondary 42B15; 47B38; 42B30; 58J40
Key Words and Phrases: fractional power dissipative operator; saturation of approximation; Sobolev type Hp space; Hadamard parametrix construction; compact manifolds

Acknowledgements

Y. Pan was supported partially by the Natural Science Foundation from the Education Department of Anhui Province (No. KJ2017A847). D. Fan was supported partially by National Natural Science Foundation of China (Grant No. 11471288, 11971295) and Natural Science Foundation of Shanghai (No. 19ZR1417600). J. Zhao was supported by the Natural Science Foundation of Zhejiang (No. LQ20A010003).

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Received: 2020-03-24
Revised: 2021-07-11
Published Online: 2021-08-23
Published in Print: 2021-08-26

© 2021 Diogenes Co., Sofia

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https://doi.org/10.1515/fca-2021-0049
Keywords for this article
fractional power dissipative operator; saturation of approximation; Sobolev type Hp space; Hadamard parametrix construction; compact manifolds

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 24–4–2021)
  4. Research Paper
  5. Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas
  6. Tutorial paper
  7. The bouncing ball and the Grünwald-Letnikov definition of fractional derivative
  8. Research Paper
  9. Fractional diffusion-wave equations: Hidden regularity for weak solutions
  10. Censored stable subordinators and fractional derivatives
  11. Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem
  12. Multivariable fractional-order PID tuning by iterative non-smooth static-dynamic H∞ synthesis
  13. Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity
  14. The rate of convergence on fractional power dissipative operator on compact manifolds
  15. Fractional Langevin type equations for white noise distributions
  16. Local existence and non-existence for a fractional reaction–diffusion equation in Lebesgue spaces
  17. Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function
  18. The Crank-Nicolson type compact difference schemes for a loaded time-fractional Hallaire equation
  19. Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework
  20. Properties of the set of admissible “state control” pair for a class of fractional semilinear evolution control systems
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