Abstract
In this paper, we introduce the definition of abstract Hardy spaces with variable exponents via the atomic decomposition and molecular decomposition. We prove the continuity from our variable Hardy space Hatop(⋅) into Lp(⋅), where p(⋅):Rn→(0,1],0<p−⩽p+⩽1. Moreover, we investigate the bilinear theory. Finally, we give an application of the abstract Hardy spaces with variable exponents.
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