학술저널
ON EQUIVALENT NORMS TO BLOCH NORM IN C
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 19, No. 4
-
2006.121 - 10 (10 pages)
- 2
For f ∈ L 2 (B, dν), k f k BM O = g |f | 2 (z) − |˜f (z)| 2 . For f continuous on B, k f k BO = sup{w(f )(z) : z ∈ B} where w(f )(z) = sup{|f (z) − f (w)| : β(z, w) ≤ 1}. In this paper, we will show that if f ∈ BM O, then k f k BO ≤ M k f k BM O . We will also show that if f ∈ BO, then k f k BM O ≤ M k f k 2 BO . A holomorphic function f : B → C is called a Bloch function (f ∈ B) if k f k B = sup z∈B Qf (z) < ∞. In this paper, we will show that if f ∈ B, then k f k BO ≤k f k B . We will also show that if f ∈ BM O and f is holomorphic, then k f k 2 B ≤ M k f k BM O .
1. Introduction
2. Relationship between k f k BM O and k f k 2
BO
3. Equivalent norms to k f k B
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