On the sharp second order Caffarelli–Kohn–Nirenberg inequality

Authors

  • Anh Tuan Duong Hanoi University of Science and Technology, Faculty of Mathematics and Informatics
  • Van Hoang Nguyen FPT University, Department of Mathematics
DOI: https://doi.org/10.54330/afm.161506

Keywords:

Caffarelli–Kohn–Nirenberg inequalities, uncertainty principle, sharp constants, extremal functions

Abstract

The purpose of this paper is twofold. By developing a new technique, we first prove some sharp Caffarelli–Kohn–Nirenberg inequalities of second order for non-radial functions. As a direct consequence, we recover the sharp second order uncertainty principle in Cazacu, Flynn and Lam (2022). For the class of radial functions, we next establish a sharp inequality which can be regarded as the second order version of Xia's inequality (2007).
Issue
Vol. 50 No. 1 (2025)
Section
Articles

Published

2025-05-06

How to Cite

Duong, A. T., & Nguyen, V. H. (2025). On the sharp second order Caffarelli–Kohn–Nirenberg inequality. Annales Fennici Mathematici, 50(1), 275–286. https://doi.org/10.54330/afm.161506

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