A^p_α spaces in the Dirichlet range are not vector spaces for p ≠ 2 and their norms are not monotone in p, via equivalent Poisson integral and inner-outer factor characterizations.
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$A^p_\alpha$ classes in the Dirichlet range: inner-outer factorization, Carleson measures and weak products
A^p_α spaces in the Dirichlet range are not vector spaces for p ≠ 2 and their norms are not monotone in p, via equivalent Poisson integral and inner-outer factor characterizations.