A Review on the Lebesgue Spaces

Authors

  • Santosh Ghimire Pulchowk Campus, Institue of Engineering, Tribhuvan University, Nepal Author
  • Bimala Mishra Central Department of Mathematics, Tribhuvan University, Nepal Author

DOI:

https://doi.org/10.3126/jsce.v9i9.46293

Keywords:

Lebesgue space, Interpolation, Hardy-Littlewood maximal function, Duality

Abstract

In this article, we begin with classical Lebesgue spaces Lp with p being constant and review the various properties such as completeness and duality of the space. To this end, we also discuss the boundedness of Hardy-Littlewood maximal function and interpolation on such spaces. Finally, we focus our attention on variable exponent Lebesgue spaces and review various results on it. Moreover, we also see the differences in between these Lebesgue spaces.

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Published

2021-12-31

Issue

Vol. 9 (2021)

Section

Research Papers

Categories

License

Copyright (c) 2021 Khwopa Engineering College and Khwopa College of Engineering

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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How to Cite

Ghimire, S., & Mishra, B. (2021). A Review on the Lebesgue Spaces. Journal of Science and Engineering (JScE), 9, 16-21. https://doi.org/10.3126/jsce.v9i9.46293