Musielak-Orlicz Campanato Spaces and Applications

By Yiyu Liang, Dachun Yang. 2013

66 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ffcca4a6c7e96fdb7c50186659d7a0a5e2f4c105

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In Applied Mathematics

  1. Dachun Yang
  2. Wen Yuan
  3. Long Huang
  4. Jun Liu
  5. Yangyang Zhang
  6. Yoshihiro Sawano
  7. Songbai Wang
  8. Ciqiang Zhuo

In Mathematical Physics

  1. Dachun Yang
  2. Wen Yuan
  3. Jun Liu
  4. Long Huang
  5. Yoshihiro Sawano
  6. Ciqiang Zhuo
  7. Yangyang Zhang
  8. Songbai Wang

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