Abstract—In this article, we present the sufficient and necessary conditions for Holder's inequality in weighted Orlicz spaces and in their weak type. One of the keys to prove our results is to estimate the norms of characteristic function in ℝⁿ.

Index Terms—Holder’s inequality, Orlicz spaces, weighted Orlicz spaces.

Al Azhary Masta and Siti Fatimah are with Department of Mathematics Education, Universitas Pendidikan Indonesia, Bandung, Indonesia (email: alazhari.masta@upi.edu).
Ifronika is with Analysis and Geometry Research Group, Institut Teknologi Bandung, Bandung, West Java, Indonesia.

Cite: Al Azhary Masta, Ifronika, Siti Fatimah, "Sufficient and Necessary Conditions for Holder’s Inequality in Weighted Orlicz Spaces," International Journal of Applied Physics and Mathematics vol. 10, no. 1, pp. 25-32, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).