Geodesic
On some Carlson-type inequalities
Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 431-444

Voir la notice de l'article provenant de la source Math-Net.Ru

We find the sharp constant in the inequality $$ \|w(\cdot) x(\cdot)\|_{L_q(T)}\le K\|w_0(\cdot) x(\cdot)\|_{L_p(T)}^{\gamma}\biggl(\sum_{j=1}^d\|\varphi_j(\cdot) x(\cdot)\|_{L_r(T)}^r\biggr)^{(1-\gamma)/r}, $$ where $T$ is a cone in $\mathbb R^d$ and the weights $w(\cdot)$, $w_0(\cdot)$ and $\varphi_j(\cdot)$, $j=1,\dots,d$, are homogeneous measurable functions. We also obtain similar inequalities for some differential operators. Bibliography: 7 titles.
Keywords: sharp inequalities, differential operators, Carlson-type inequalities. 
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     author = {K. Yu. Osipenko},
     title = {On some {Carlson-type} inequalities},
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K. Yu. Osipenko. On some Carlson-type inequalities. Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 431-444. http://geodesic.mathdoc.fr/item/SM_2025_216_3_a10/