Musielak-Orlicz Campanato Spaces and Applications

Original · EN

Let φ: Rⁿ× [0,∞)→[0,∞) be such that φ(x,·) is an Orlicz function and φ(·,t) is a Muckenhoupt A∞(Rⁿ) weight uniformly in t. In this article, the authors introduce the Musielak-Orlicz Campanato space Lᵩ,q,ₛ(Rⁿ) and, as an application, prove that some of them is the dual space of the Musielak-Orlicz Hardy space Hφ(Rⁿ), which in the case when q=1 and s=0 was obtained by L. D. Ky [arXiv: 1105.0486]. The authors also establish a John-Nirenberg inequality for functions in Lᵩ,₁,ₛ(Rⁿ) and, as an application, the authors also obtain several equivalent characterizations of Lᵩ,q,ₛ(Rⁿ), which, in return, further induce the φ-Carleson measure characterization of Lᵩ,₁,ₛ(Rⁿ).