Bounded projections in weighted function spaces in a generalized unit disc

• Autorzy: A. H. Karapetyan
• Języki publikacji: EN

Abstrakty

EN

Let $M_{m,n}$ be the space of all complex m × n matrices. The generalized unit disc in $M_{m,n}$ is >br>    $R_{m,n} = {Z ∈ M_{m,n}: I^{(m)} - ZZ* is positive definite}$.
Here $I^{(m)} ∈ M_{m,m}$ is the unit matrix. If 1 ≤ p < ∞ and α > -1, then $L^{p}_{α}(R_{m,n})$ is defined to be the space $L^p{R_{m,n}; [det(I^{(m)} - ZZ*)]^α dμ_{m,n}(Z)}$, where $μ_{m,n}$ is the Lebesgue measure in $M_{m,n}$, and $H^p_α(R_{m,n}) ⊂ L^{p}_{α}(R_{m,n})$ 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(𝒵)= T^{β}_{m,n}(f)(𝒵), 𝒵 ∈ R_{m,n},
where $T^{β}_{m,n}$ 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 $T^{β}_{m,n}$ to be a bounded projection of $L^p_α(R_{m,n})$ onto $H^p_α(R_{m,n})$. Some applications of this result are given.

Słowa kluczowe

EN

generalized unit disc   holomorphic and pluriharmonic functions   weighted spaces   integral representations   bounded integral operators  

Kategorie tematyczne

• 45P05: Integral operators
• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions
• 32A10: Holomorphic functions
• 31C10: Pluriharmonic and plurisubharmonic functions
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)
• 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 3
• Strony: 193-218

Daty

wydano

1995

otrzymano

1993-04-14

Twórcy

autor

A. H. Karapetyan

• Institute of Mathematics, Armenian Academy of Sciences, Marshal Bagramian Ave. 24 B, Erevan 375019, Armenia

Bibliografia

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