The diagonal mapping in mixed norm spaces
Guangbin Ren ; Jihuai Shi
Studia Mathematica, Tome 162 (2004), p. 103-117 / Harvested from The Polish Digital Mathematics Library
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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 Hp,q,α(Uⁿ) of the polydisc onto the mixed norm space Hp,q,|α|+(p/q+1)(n-1)(U) of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:285314 
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Guangbin Ren; Jihuai Shi. The diagonal mapping in mixed norm spaces. Studia Mathematica, Tome 162 (2004) pp. 103-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-1/