Hardy and BMO spaces associated with new Muckenhoupt‐type weights in the Bessel setting

Abstract 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 .