Harmonic Besov spaces on the ball (Q2822020)

The authors study the properties of Besov spaces of harmonic functions on the unit ball \(\mathbb{B}\). They introduce the (two-parameter) harmonic Besov spaces \(b_q^p\) and they show several equivalent characterizations of such spaces. They prove that the spaces \(b^2_q\) are reproducing kernel Hilbert spaces. Then they consider the Bergman-Besov projections from a certain (weighted) Lebesgue spaces \(L^p_q\) onto \(b^p_q\) and show necessary and sufficient conditions for their boundedness.