论文标题
Lebesgue空间中功能的指数近似
Exponential approximation of functions in Lebesgue spaces with Muckenhoupt weight
论文作者
论文摘要
使用转移结果，在$ \ MATHCAL {C}（\ MATHBF {r}）$中，通过指数类型的整个功能的几个近似不等式，在$ \ Mathbf {r}上定义的有限连续函数类别的类别$ l^{p} \ left（\ mathbf {\ varrho} dx \ right）$ 1 \ leq p <\ infty $带有muckenhoupt stroge $ \ mathbf {\ mathbf {\ varrho} $（$ 1 \ leq p <\ infty $）。这为我们提供了杰克逊类型的直接定理和伯恩斯坦 - timan类型的反向估计的不同证明，$ l^{p} \ left（\ mathbf {\ varrho} dx \ right）$。结果还涵盖了案例$ p = 1 $。
Using a transference result, several inequalities of approximation by entire functions of exponential type in $\mathcal{C}(\mathbf{R})$, the class of bounded uniformly continuous functions defined on $\mathbf{R}:=\left( -\infty ,+\infty \right) $, are extended to the Lebesgue spaces $L^{p}\left( \mathbf{\varrho }dx\right) $ $1\leq p<\infty $ with Muckenhoupt weight $\mathbf{\varrho }$ ($1\leq p<\infty $). This gives us a different proof of Jackson type direct theorems and Bernstein-Timan type inverse estimates in $L^{p}\left( \mathbf{\varrho }dx\right) $. Results also cover the case $p=1$.
