Normal bases for non-archimedean spaces of continuous functions.
Let K be a non-archimedean valued field which contains Qp and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn|n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq → K) is the Banach space of continuous functions from Vq to K, equipped with the supremum norm. Our aim is to find normal bases (rn(x)) for C(Vq → K), where rn(x) does not have to be a polynomial.
Let denote the usual Hardy space of analytic functions on the unit disc . We prove that for every function there exists a linear operator defined on which is simultaneously bounded from to and from to such that . Consequently, we get the following results :1) is a Calderon-Mitjagin couple;2) for any interpolation functor , we have , where denotes the closed subspace of of all functions whose Fourier coefficients vanish on negative integers.These results also extend to Hardy...
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