Science China Mathematics

, Volume 62, Issue 1, pp 73–124 | Cite as

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

  • Víctor Almeida
  • Jorge J. Betancor
  • Alejandro J. Castro
  • Lourdes Rodríguez-MesaEmail author


In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.


graphs discrete Laplacian Hardy spaces variable exponent square functions spectral multipliers 


42B30 42B35 60J10 


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The first, second and fourth authors are partially supported by Spanish Government Grant (Grant No. MTM2016-79436-P). The third author is also supported by Nazarbayev University Social Policy Grant. The authors would strongly like to give thanks to Professor Dachun Yang for sending us his paper [64] (jointly with C. Zhuo and Y. Sawano). Also, the authors are grateful to the referees for the careful reading of the manuscript.


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Víctor Almeida
    • 1
  • Jorge J. Betancor
    • 1
  • Alejandro J. Castro
    • 2
  • Lourdes Rodríguez-Mesa
    • 1
    Email author
  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaLa LagunaSpain
  2. 2.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

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