Bergman Type Projection on Lipschitz Spaces

On the unit ball of $${\mathbb{R}}^{n}$$ , some Bergman type operators are defined with the use of fractional derivatives and reproducing kernels of Poisson–Bergman type, which act boundedly in the Lipschitz spaces. In a special case, these operators continuously map the Lipschitz space of sufficiently smooth functions onto its harmonic subspace.