Abstract
If N ∈ ℕ, 0 < p ≤ 1, and(Xk) Nk=1 are r.i.p-spaces, it is shown that there is C(= C(p, N)) > 0, such that for every ƒ ∈ ∩ Nk=1 Xk, there exists\(\bar f \in \bigcap\nolimits_{k = 1}^N {H(X_k )} \) with\(||f - \tilde f||X_k \leqslant C \cdot distX_k (f,H(X_k )),\), for every 1 ≤ k ≤ N. Also, if ⊓ is a convex polygon in ℝ2, it is proved that the N-tuple (H(X1),…, H(Xn)) is K⊓-closed with respect to (X1,…, XN) in the sense of Pisier. Everything follows from Theorem 2.1, which is a general analytic partition of unity type result.
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Communicated by Jose Garcia-Cuerva
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Muscalu, C. A joint norm control Nehari type theorem forN-tuples of Hardy spaces. J Geom Anal 9, 683–691 (1999). https://doi.org/10.1007/BF02921979
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DOI: https://doi.org/10.1007/BF02921979