Musielak-Orlicz Campanato Spaces and Applications

Abstract

Let $\phi :{\mathbb{R}}^n\times [0,\infty )\to [0,\infty )$ be such that $\phi (x,\cdot )$ is an Orlicz function and $\phi (\cdot ,t)$ is a Muckenhoupt $A_{\infty }({\mathbb{R}}^n)$ weight uniformly in $t$. In this article, the authors introduce the Musielak-Orlicz Campanato space ${\mathcal{L}}_{\phi ,q,s}({\mathbb{R}}^n)$ and, as an application, prove that some of them is the dual space of the Musielak-Orlicz Hardy space $H^{\phi }({\mathbb{R}}^n)$, 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 ${\mathcal{L}}_{\phi ,1,s}({\mathbb{R}}^n)$ and, as an application, the authors also obtain several equivalent characterizations of ${\mathcal{L}}_{\phi ,q,s}({\mathbb{R}}^n)$, which, in return, further induce the $\phi$-Carleson measure characterization of ${\mathcal{L}}_{\phi ,1,s}({\mathbb{R}}^n)$.

References in corpus (1)

• Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

Cited by in corpus (2)

• Musielak-Orlicz BMO-Type Spaces Associated with Generalized Approximations to the Identity
• On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces