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Equivalent characterizations of Bloch functions

100%

Hu Z.

Colloquium Mathematicum

1994

tom 67

nr 1

99-108

In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].

Estimates for the integral means of holomorphic functions on bounded domains in $ℂ^{n}$

100%

Hu Z.

Colloquium Mathematicum

1996

tom 69

nr 2

213-238

Let 𝓓 = {z ∈ ℂ^{n} : λ(z) < 0} be a bounded domain with $C^{∞}$ boundary. For f holomorphic in 𝓓, let $M_{p}(f,r)$ be the pth integral mean of f on $∂𝓓_{r}= {z ∈ 𝓓 : λ(z)=-r}$. In this paper we prove that $ ∫_{0}^{ε} r^{s+|α|q} M_{p}^{q}(D^{α}f,r)dr ≤ C ∫_{0}^{ε} r^{s}M_{p}^{q}(f,r)dr$ and $ ∫_{0}^{ε} r^{s} M_{p}^{q}(f,r)dr ≤ C { ∑_{|α|-1, m ∈ ℕ, α =(α_{1},...,α_{n}) is a multi-index, and ε > 0 is small enough. These inequalities generalize the known results in [9,10] on the unit ball of $ℂ^{n}$. Two applications are given. The methods used in the proof of the inequalities also enable us to obtain some theorems about pluriharmonic functions on 𝓓.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Hu Z.

1 1996

1 1994

Wyniki wyszukiwania

Equivalent characterizations of Bloch functions

Estimates for the integral means of holomorphic functions on bounded domains in $ℂ^{n}$