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arXiv · 2606.09067

On the Constant and Extremal Function for Weighted Hardy Inequality in $L_p$

Ivan Gadjev
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Abstract

We study the behaviour of the smallest possible constant $d(a,b, p,\epsilon)$ in Hardy inequality $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^px^{\epsilon}\,dx\leq d(a,b,p,\epsilon)\,\int_a^b [f(x)]^px^{\epsilon}\, dx, \quad 2\le p<\infty. $$ The exact rate of convergence of $d(a,b,p,\epsilon)$ is established and the ``almost extremal'' function is found.

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Ivan Gadjev. 2026-06-08. On the Constant and Extremal Function for Weighted Hardy Inequality in $L_p$. https://arxiv.org/abs/2606.09067

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