Geodesic
Sharp Carlson Type Inequalities with Many Weights
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 229-240

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The paper is concerned with sharp Carlson type inequalities of the form $$\|w(\cdot) x(\cdot)\|_{L_q(T)}\le K\|w_0(\cdot) x(\cdot)\|_{L_p(T)}^{\gamma}\max_{1\le j\le n}\|w_j(\cdot) x(\cdot)\|_{L_r(T)}^{1-\gamma},$$ where $T$ is a cone in $\mathbb R^d$ and the weight functions $w_j(\cdot)$, $j=1,\ldots,n$, are homogeneous with some symmetry property.
Keywords: Carlson type inequalities
Mots-clés : sharp constants. 
@article{TIMM_2023_29_4_a18,
     author = {K. Yu. Osipenko},
     title = {Sharp {Carlson} {Type} {Inequalities} with {Many} {Weights}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {229--240},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a18/}
}
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K. Yu. Osipenko. Sharp Carlson Type Inequalities with Many Weights. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 229-240. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a18/