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Variable exponent Hardy spaces associated with discrete Laplacians on graphs

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, 38721, Spain

    Víctor Almeida, Jorge J. Betancor & Lourdes Rodríguez-Mesa

  2. Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan

    Alejandro J. Castro

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  1. Víctor Almeida
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  2. Jorge J. Betancor
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  4. Lourdes Rodríguez-Mesa
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Correspondence to Lourdes Rodríguez-Mesa.

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Almeida, V., Betancor, J.J., Castro, A.J. et al. Variable exponent Hardy spaces associated with discrete Laplacians on graphs. Sci. China Math. 62, 73–124 (2019). https://doi.org/10.1007/s11425-017-9200-2

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