The diagonal mapping in mixed norm spaces

• Autorzy: Guangbin Ren , Jihuai Shi
• Języki publikacji: EN

Abstrakty

EN

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 𝓓F(z) = F(z,...,z), and prove that the diagonal mapping 𝓓 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 ≤ ∞.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 163
• Numer: 2
• Strony: 103-117

Daty

wydano

2004

Twórcy

autor

Guangbin Ren

• Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
• Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

autor

Jihuai Shi

• Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Identyfikatory

DOI

10.4064/sm163-2-1