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John–Nirenberg Type Inequalities for Musielak–Orlicz Campanato Spaces on Spaces of Homogeneous Type

  • Duong Quoc Huy
  • Luong Dang KyEmail author
Article
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Abstract

Let X be a space of homogeneous type in the sense of Coifman and Weiss. Let φ : X × [0, ) → [0, ) be such that φ(x,⋅) is an Orlicz function and φ(⋅, t) is a Muckenhoupt A(X) weight uniformly in t. In this paper, we propose John–Nirenberg type inequalities for Musielak–Orlicz Campanato spaces on spaces of homogeneous type. As an application, we show the coincidence between the space BMO(X) and the weighted space BMOw(X) whenever wA(X).

Keywords

Musielak–Orlicz function BMO space Campanato space John–Nirenberg inequality Spaces of homogeneous type 

Mathematics Subject Classification (2010)

43A85 46E30 

Notes

Acknowledgements

The authors would like to thank the referees for their careful reading and helpful suggestions.

Funding Information

This work is supported by the Vietnam National Foundation for Science and Technology Development (Grant No. 101.02-2016.22)

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Natural Science and TechnologyTay Nguyen UniversityDak LakVietnam
  2. 2.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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