From dyadic Λα to Λα
نویسنده
چکیده
In this paper we show how to compute the Λα norm , α ≥ 0, using the dyadic grid. This result is a consequence of the description of the Hardy spaces H(R ) in terms of dyadic and special atoms. Recently, several novel methods for computing the BMO norm of a function f in two dimensions were discussed in [9]. Given its importance, it is also of interest to explore the possibility of computing the norm of a BMO function, or more generally a function in the Lipschitz class Λα, using the dyadic grid in R . It turns out that the BMO question is closely related to that of approximating functions in the Hardy space H(R ) by the Haar system. The approximation in H(R ) by affine systems was proved in [2], but this result does not apply to the Haar system. Now, if H(R) denotes the closure of the Haar system in H(R), it is not hard to see that the distance d(f,H) of f ∈ H(R) to H is ∼ ∣
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