On Cauchy and Poisson type formulas for one weighted Hardy space (in Ukrainian)

For the space of analytic in the half-plane $\mathbb C_+=\{z:\text{Re}z>0\}$ functions such that\linebreak $ \sup_{|\varphi|<\frac{\pi}{2}}\big\{\int_0^{+\infty} |f(re^{i\varphi})|^pe^{-p\sigma r|\sin \varphi|}dr\big\}^{1/p}<+\infty$ we obtain the representation formula\linebreak $ -\frac{1}{2\pi }\int_{0}^{+\infty}\frac{f(iv)e^{-i\sigma(z-iv)}}{iv-z}dv-\frac{1}{2\pi }\int_{-\infty}^{0}\frac{f(iv)e^{i\sigma(z-iv)}}{iv-z}dv-\frac{1}{\pi}\int_{0}^{+\infty} \frac{f(u)\sin\sigma(z-u)}{u-z}du= \begin{cases} f(z), z\in \mathbb C_+, \\ 0,\ z\in\ \mathbb C \setminus\overline{\mathbb{C}}_{+} \end{cases} $ and an analogue of the Poisson integral. These results are true for usual Hardy space also.