On harmonic function spaces. II. (English) Zbl 1143.31002
The author investigates several spaces of harmonic functions, including Bloch, Hardy, weighted Bergman, Besov and Dirichlet spaces on the unit ball in \(\mathbb R^n\). The paper studies the relationships among the above spaces as well as equivalent conditions for harmonic Bergman and Besov spaces. Section 5 of the paper includes several results concerning harmonic functions whose homogeneous polynomial expansion has Hadamard gaps.
Reviewer: Manfred Stoll (Columbia)
MSC:
31B05 | Harmonic, subharmonic, superharmonic functions in higher dimensions |
31C25 | Dirichlet forms |
46E15 | Banach spaces of continuous, differentiable or analytic functions |