A (p, q) version of Bourgain’s theorem
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چکیده
Let 1 < p, q < ∞ satisfy 1 p + 1 q = 1. We construct an orthonormal basis {bn} for L(R) such that ∆p(bn) and ∆q(c bn) are both uniformly bounded in n. Here ∆λ(f) ≡ infa∈R `R |x − a||f(x)|dx ́ 1 2 . This generalizes a theorem of Bourgain and is closely related to recent results on the Balian-Low theorem.
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تاریخ انتشار 2006