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The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space H p , q , α ( U ) of the polydisc onto the mixed norm space H p , q , | α | + ( p / q + 1 ) ( n - 1 ) ( U ) of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

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