Weighted Banach spaces of harmonic functions (Q740692)

The authors study Banach spaces of harmonic functions on open sets of \(\mathbb R^N\) or \(\mathbb C^N\) endowed with weighted supremum norms. The harmonic associated weight is introduced and investigated in these spaces, extending the work on the corresponding spaces of holomorphic functions due to \textit{K. D. Bierstedt} et al. [Stud. Math. 127, No. 2, 137--168 (1998; Zbl 0934.46027)]. They also characterize the boundedness and estimate the essential norm of a composition operator acting on weighted spaces of pluriharmonic functions.