We study uniform approximation in the open unit disc ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn2.gif] {$D=\{z\colon |z|<1\}$} by logarithmic derivatives of ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn3.gif] {$C$} -polynomials, that is, polynomials whose zeros lie on the unit circle ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn4.gif] {$C=\{z\colon |z|\,{=}\,1\}$} . We find bounds for the rate of approximation for functions in Hardy class ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn5.gif] {$H^1(D)$} and certain subclasses. We prove bounds for the rate of uniform approximation (either in ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn6.gif] {$D$} or its closure) by ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_...] {$h$}

中文翻译：

---

关于## IMG ##的单位磁盘中的近似速率[http://ej.iop.org/images/1064-5632/84/3/437/toc_IZV_84_3_437ie​​qn1.gif] {$ H ^ 1 $}-边界为零的多项式的对数导数的函数

我们在开放式单元光盘## IMG ## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ie​​qn2.gif]中研究均匀近似，{$ D = \ {z \冒号| z | <1 \} $}由## IMG ##的对数导数[http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ie​​qn3.gif] {$ C $} -多项式，即零位于单位圆上的多项式## IMG ## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ie​​qn4.gif] {$ C = \ {z \冒号| z | \，{=} \，1 \} $}。我们在Hardy类## IMG ## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ie​​qn5.gif] {$ H ^ 1中找到函数近似率的界线（D）$}和某些子类。我们证明了统一近似率的界线（在## IMG ## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ie​​qn6.gif] {$ D $}或它的关闭）＃＃IMG ## [http：//ej.iop.org/images/1064-5632/84/3/437/IZV_84 _...