Year: 2026
Type: article
Abstract: We obtain a family of improved Hardy, Leray, and Poincaré inequalities for $$2 \le p < n$$ 2 ≤ p < n , incorporating explicit multidimensional remainder terms. These inequalities feature additive contributions of the form $$\sum _{i=1}^n x_i^{-p}$$ ∑ i = 1 n x i - p with an explicit constant that depends only on p , independent of the dimension n . We establish that the structural factor $$\big (\tfrac{p-1}{p}\big )^p$$ ( p - 1 p ) p appearing in the remainder term of the Hardy inequality is sharp. The results extend known cases beyond $$L^2$$ L 2 , unify different inequalities under a common framework, and yield stronger remainder estimates. They also provide a foundation for further generalizations to weighted and singular settings.
Author: Sumeyye Bakim
Institution: KTO Karatay University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7154448104