Littlewood--Paley characterizations of BMO and Triebel--Lizorkin spaces
Abstract
We prove one generalization of the Littlewood--Paley characterization of the BMO space where the dilations of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel--Lizorkin spaces can be characterized in a similar way.
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