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Introduces Hardy spaces with new weights, characterizes them via atoms, and shows application with Carleson characterization.
We introduce the Hardy spaces with in the new weights , , associated with the Bessel operator Then we establish equivalent characterizations of via atoms and maximal functions. We also introduce the weighted space and establish the duality of and for . As an application, we show a ‐Carleson characterization of with via the Poisson semigroup .
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Guo et al. (2025) studied this question.
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