Pointwise multipliers on Orlicz-Campanato spaces

• Published in: Journal of functional analysis Vol. 284; no. 7; p. 109824
• Main Authors: Fang, Chenglong, Liu, Liguang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2023
• Subjects: BMO space; Campanato space; Orlicz space; Pointwise multipliers; 42B35; BMO space; 46E30; Campanato space; Pointwise multipliers; Orlicz space; 42B15
• ISSN: 0022-1236; 1096-0783
• DOI: 10.1016/j.jfa.2022.109824

Let ψ:(0,∞)→(0,∞) be a non-decreasing function with critical lower and upper type indices σ−⁎ and σ+⁎. Given a Campanato type space Cψ(Rn) that was defined associated to the function ψ, under σ−⁎>⌊σ+⁎⌋−1 when n≥2 or σ−⁎>σ+⁎−1 when n=1, the authors prove that any function is a pointwise multiplier on Cψ(Rn) if and only if it is bounded and belongs to a Musielak-Orlicz-Campanato space CΨ(Rn) that was associated toΨ(x,r):=|∫r1ψ(t)dtt|+∫1max⁡{r,e+|x|}(max⁡{r,e+|x|}t)⌊σ+⁎⌋ψ(t)dtt, where x∈Rn and r∈(0,∞). This generalizes the known characterizations of pointwise multipliers on the BMO(Rn) space and the Campanato space.