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Function algebras of Besov and Triebel-Lizorkin-type

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Abstract

We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.

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References

  1. F. Bensaid, M. Moussai: Realizations of the homogeneous Besov-type spaces. Methods Appl. Anal. 26 (2019), 349–370.

    Article  MathSciNet  Google Scholar 

  2. G. Bergh, J. Löfström: Interpolation Spaces: An Introduction. Grundlehren der mathematischen Wissenschaften 223. Springer, Berlin, 1976.

    Google Scholar 

  3. G. Bourdaud, M. Moussai, W. Sickel: Composition operators on Lizorkin-Triebel spaces. J. Funct. Anal. 259 (2010), 1098–1128.

    Article  MathSciNet  Google Scholar 

  4. G. Bourdaud, M. Moussai, W. Sickel: Composition operators acting on Besov spaces on the real line. Ann. Mat. Pura Appl. (4) 193 (2014), 1519–1554.

    Article  MathSciNet  Google Scholar 

  5. A. El Baraka: An embedding theorem for Campanato spaces. Electron. J. Differ. Equ. 66 (2002), Article ID 66, 17 pages.

  6. M. Frazier, B. Jawerth: Decomposition of Besov spaces. Indiana Univ. Math. J. 34 (1985), 777–799.

    Article  MathSciNet  Google Scholar 

  7. M. Moussai: Composition operators on Besov algebras. Rev. Mat. Iberoam. 28 (2012), 239–272.

    Article  MathSciNet  Google Scholar 

  8. M. Moussai: Realizations of homogeneous Besov and Triebel-Lizorkin spaces and an application to pointwise multipliers. Anal. Appl., Singap. 13 (2015), 149–183.

    Article  MathSciNet  Google Scholar 

  9. M. Moussai: Composition operators on Besov spaces in the limiting case s = 1 + Stud. Math. 241 (2018), 1–15.

    MathSciNet  Google Scholar 

  10. J. Peetre: New Thoughts on Besov Spaces. Duke University Mathematics Series I. Duke University, Durham, 1976.

    Google Scholar 

  11. T. Runst, W. Sickel: Sobolev Spaces of Fractional Order, Nemytskij Operators and Nonlinear Partial Differential Equations. de Gruyter Series in Nonlinear Analysis and Applications 3. Walter de Gruyter, Berlin, 1996.

    Book  Google Scholar 

  12. H. Triebel: Theory of Function Spaces. Monographs in Mathematics 78. Birkhäuser, Basel, 1983.

    Book  Google Scholar 

  13. H. Triebel: Theory of Function Spaces II. Monographs in Mathematics 84. Birkhäuser, Basel, 1992.

    Book  Google Scholar 

  14. D. Yang, W. Yuan: New Besov-type spaces and Triebel-Lizorkin-type spaces including Q spaces. Math. Z. 265 (2010), 451–480.

    Article  MathSciNet  Google Scholar 

  15. W. Yuan, W. Sickel, D. Yang: Morrey and Campanato Meet Besov, Lizorkin and Triebel. Lecture Notes in Mathematics 2005. Springer, Berlin, 2010.

    Google Scholar 

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Acknowledgments

The authors thank both the referee for valuable comments and suggestions, and the General Direction of Scientific Research and Technological Development DGRSDT-Algeria.

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Authors and Affiliations

  1. Laboratory of Functional Analysis and Geometry of Spaces, M. Boudiaf University of M’Sila, 28000, M’Sila, Algeria

    Fares Bensaid & Madani Moussai

  2. Department of Mathematics, University of Bordj Bou-Arreridj, 34030, Bordj Bou-Arreridj, Algeria

    Fares Bensaid

Authors
  1. Fares Bensaid
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  2. Madani Moussai
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Correspondence to Madani Moussai.

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Bensaid, F., Moussai, M. Function algebras of Besov and Triebel-Lizorkin-type. Czech Math J 73, 1281–1300 (2023). https://doi.org/10.21136/CMJ.2023.0585-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0585-22

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