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In this article we define the Calderón-Hardy spaces with variable exponents on Rn , H p(.) q,γ (Rn) , and we show that for m∈N the operator Δm is a bijective mapping from H p(.) q,2m(R) onto Hp(.)(Rn) . Mathematics subject classification (2010): 42B25, 42B30.

Calderón-Hardy Spaces with variable exponents and the solution of the equation Δ^m F = f for f ∈ H^p(⋅)(ℝ^n)