By means of Muckenhoupt type conditions, we characterize the weights ω on $\mathbb{C}$ such that the Bergman projection of $F_{\alpha }^{2,\ell }=H(\mathbb{C})\cap L^2(\mathbb{C},e^{-\frac{\alpha }{2}|z{|}^{2\ell }})$, $\alpha >0$, $\ell >1$, is bounded on $L^p(\mathbb{C},e^{-\frac{\alpha p}{2}|z{|}^{2\ell }}\omega (z))$, for $1<p<\infty$. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces $A^p(\omega )=H(\mathbb{C})\cap L^p(\omega )$. Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces $F_{\alpha }^{p,\ell }=H(\mathbb{C})\cap L^p(\mathbb{C},e^{-\frac{\alpha p}{2}|z{|}^{2\ell }})$.

中文翻译：

---

伯格曼空间的 Muckenhoupt 类型权重和 Berezin 公式

通过 Muckenhoupt 类型条件，我们表征了权重ω on$\mathbb{C}$ 使得 Bergman 投影 $F_{\alpha }^{2,\ell }=H(\mathbb{C})\cap {升}^2(\mathbb{C},{\mathrm{电子}}^{-\frac{\alpha }{2}|z{|}^{2\ell }})$, $\alpha >0$, $\ell >1$, 有界于 ${升}^{磷}(\mathbb{C},{\mathrm{电子}}^{-\frac{\alpha 磷}{2}|z{|}^{2\ell }}\omega (z))$， 为了 $1<磷<\infty$. 我们还获得了加权伯格曼空间中函数的显式表示积分公式${\mathrm{一种}}^{磷}(\omega )=H(\mathbb{C})\cap {升}^{磷}(\omega )$. 最后，我们检验了关于空间上某些 Toeplitz 算子的乘积有界性的所谓 Sarason 猜想的有效性$F_{\alpha }^{磷,\ell }=H(\mathbb{C})\cap {升}^{磷}(\mathbb{C},{\mathrm{电子}}^{-\frac{\alpha 磷}{2}|z{|}^{2\ell }})$.