Derivatives of Harmonic Bergman and Bloch Functions on the Ball

On the setting of the unit ball of euclidean n-space, we investigate properties of derivatives of functions in the harmonic Bergman space and the harmonic Bloch space. Our results are (1) size estimates of derivatives of the harmonic Bergman kernel, (2) Gleason’s problem, and (3) characterizations in terms of radial, tangential, and ordinary derivative norms. In the course of proofs, some reproducing formulas are found and estimated.