An integral representation for Besov and Lipschitz spaces

It is well known that functions in the analytic Besov space $B_1$ on the unit disk $\text{D}$ admits an integral representation $$f(z)=\text{ind}\frac{z-w}{1-z\bar{w}}d\mu (w),$$ where $\mu$ is a complex Borel measure with $\mathrm{\mid }\mu \mathrm{\mid }(\text{D})<\mathrm{\infty }$. We generalize this result to all Besov spaces $B_p$ with $0<p\le 1$ and all Lipschitz spaces ${\mathrm{\Lambda }}_t$ with $t>1$. We also obtain a version for Bergman and Fock spaces.