Harmonic approximation by finite sums of moduli

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Doubtsov, Evgueni^1,2 

[1] VA Steklov Math Inst, St Petersburg Dept, St Petersburg 191023, Russia

[2] St Petersburg State Univ, Dept Math & Mech, St Petersburg 198504, Russia

关键词: Harmonic growth space;    Harmonic approximation;    Radial weight;    Doubling weight function;    Log-convex weight function;   

DOI  :  10.1016/j.jmaa.2015.04.095

来源: Elsevier

【 摘 要 】

Let h(B-d) denote the space of real-valued harmonic functions on the unit ball B-d of R-d, d >= 2. Given a radial weight w on B-d, consider the following problem: construct a finite family {f(1), f(2),..,f(J)} in h(B-d) such that the sum vertical bar f(1)vertical bar + vertical bar f(2)vertical bar + ... + vertical bar f(J)vertical bar is equivalent to w. We solve the problem for weights w with a doubling property. Moreover, if d is even, then we characterize those w for which the problem has a solution. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free