The diagonal mapping in mixed norm spaces

Guangbin Ren, and Jihuai Shi. "The diagonal mapping in mixed norm spaces." Studia Mathematica 163.2 (2004): 103-117. <http://eudml.org/doc/285314>.

@article{GuangbinRen2004,
abstract = {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 $H^\{p,q,α\}(Uⁿ)$ 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 ≤ ∞.},
author = {Guangbin Ren, Jihuai Shi},
journal = {Studia Mathematica},
keywords = {diagonal mapping; holomorphic mixed norm space; weighted Bergman projections},
language = {eng},
number = {2},
pages = {103-117},
title = {The diagonal mapping in mixed norm spaces},
url = {http://eudml.org/doc/285314},
volume = {163},
year = {2004},
}

TY - JOUR
AU - Guangbin Ren
AU - Jihuai Shi
TI - The diagonal mapping in mixed norm spaces
JO - Studia Mathematica
PY - 2004
VL - 163
IS - 2
SP - 103
EP - 117
AB - 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 $H^{p,q,α}(Uⁿ)$ 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 ≤ ∞.
LA - eng
KW - diagonal mapping; holomorphic mixed norm space; weighted Bergman projections
UR - http://eudml.org/doc/285314
ER -