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In this paper we develop the theory of variable exponent Hardy spacesassociated with discrete Laplacians on infinite graphs. Our Hardy spaces aredefined by square integrals, atomic and molecular decompositions. Also we studyboundedness properties of Littlewood-Paley functions, Riesz transforms, andspectral multipliers for discrete Laplacians on variable exponent Hardy spaces.

Variable exponent Hardy spaces associated with discrete Laplacians on graphs