Let $\mathbb{T}, \mathbb{D}$ be the unit circle and unit disc respectively in the complex plane $\mathbb{C}$. For $f\in L^\infty(\mathbb{T})$, the Poisson Integral map $P:L^\infty(\mathbb{T})\longrightarrow h^\infty(\mathbb{D})(f\in L^\infty(\mathbb{D})$ which are harmonic) is defined as $$P(f)(re^{i\theta})=\frac{1}{2\pi}\int_{-\pi}^{\pi}{\frac{1-r^2}{1+r^2-2cos(\theta-t)}}f(e^{it})dt\;\;\;\;\;(re^{i\theta})\in \mathbb{D}.$$ It is known that this map is onto also.
I wanted to know if $$f(0)=\frac{1}{2\pi}\int_{-\pi}^{\pi}(P^{-1}\circ f)(e^{it})dt\;\;\;\;\;f\in h^\infty(\mathbb{D}) $$ is true?