Radial growth of the derivatives of analytic functions in Besov spaces

IF 0.3 Q4 MATHEMATICS
S. Dominguez, D. Girela
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引用次数: 1

Abstract

Abstract For 1 < p < ∞, the Besov space Bp consists of those functions f which are analytic in the unit disc 𝔻 = {z ∈ 𝔺 : |z| < 1} and satisfy ∫𝔻(1 − |z|2)p−2|f ′(z)|p dA(z) < ∞. The space B2 reduces to the classical Dirichlet space 𝒟. It is known that if f ∈ 𝒟then |f ′(reiθ)| = o[(1 − r)−1/2], for almost every ∈ [0, 2π]. Hallenbeck and Samotij proved that this result is sharp in a very strong sense. We obtain substitutes of the above results valid for the spaces Bp (1 < p < ∞) an we give also an application of our them to questions concerning multipliers between Besov spaces.
Besov空间中解析函数导数的径向增长
当1 < p <∞时,Besov空间Bp由在单位圆盘上的解析函数f = {z∈𝔺:|z| < 1}且满足∫(1−|z|2)p−2|f ' (z)|p dA(z) <∞构成。空间B2简化为经典的狄利克雷空间。已知如果f∈𝒟then |f ' (reito)| = 0[(1−r)−1/2],对于几乎所有∈[0,2 π]。Hallenbeck和Samotij证明了这个结果在很强的意义上是尖锐的。我们得到了上述结果对空间Bp (1 < p <∞)有效的代换,并给出了它们在Besov空间间乘子问题上的一个应用。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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