- Tytuł:
- Bounded projections in weighted function spaces in a generalized unit disc
- Autorzy:
- Karapetyan, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/1311367.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
generalized unit disc
holomorphic and pluriharmonic functions
weighted spaces
integral representations
bounded integral operators - Opis:
- Let $M_{m,n}$ be the space of all complex m × n matrices. The generalized unit disc in $M_{m,n}$ is $R_{m,n} = {Z ∈ M_{m,n}: I^{(m)} - ZZ^\ast \text{ is positive definite} }$. Here $I^{(m)} ∈ M_{m,m}$ is the unit matrix. If 1 ≤ p < ∞ and α > -1, then $L_{α}^{p}(R_{m,n})$ is defined to be the space $L^p{R_{m,n}; [det(I^{(m)} - ZZ^\ast)]^α dμ_{m,n}(Z)}$, where $μ_{m,n}$ is the Lebesgue measure in $M_{m,n}$, and $H_α^p(R_{m,n}) ⊂ L_{α}^{p}(R_{m,n})$ is the subspace of holomorphic functions. In [8,9] M. M. Djrbashian and A. H. Karapetyan proved that, if $Reβ > (α+1)//p -1$ (for 1 < p < ∞) and Re β ≥ α (for p = 1), then $f(\mathcal{Z})= T_{m,n}^{β}(f)(\mathcal{Z}), \mathcal{Z} ∈ R_{m,n},$ where $T_{m,n}^{β}$ is the integral operator defined by (0.13)-(0.14). In the present paper, given 1 ≤ p < ∞, we find conditions on α and β for $T_{m,n}^{β}$ to be a bounded projection of $L_α^p(R_{m,n})$ onto $H_α^p(R_{m,n})$. Some applications of this result are given.
- Źródło:
-
Annales Polonici Mathematici; 1995, 62, 3; 193-218
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł