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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2023},
     volume = {29},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a18/}
}
TY  - JOUR
AU  - K. Yu. Osipenko
TI  - Sharp Carlson Type Inequalities with Many Weights
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 229
EP  - 240
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a18/
LA  - ru
ID  - TIMM_2023_29_4_a18
ER  - 
%0 Journal Article
%A K. Yu. Osipenko
%T Sharp Carlson Type Inequalities with Many Weights
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 229-240
%V 29
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a18/
%G ru
%F TIMM_2023_29_4_a18
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/

[1] Carlson F., “Une inégalité”, Ark. Mat. Astr. Fysik, 25B (1934), 1–5 | MR | Zbl

[2] Levin V.I., “Tochnye konstanty v neravenstvakh tipa Karlsona”, Dokl. AN SSSR, 59 (1948), 635–638 | Zbl

[3] Andrianov F.I., “Mnogomernye analogi neravenstva Karlsona i ego obobscheniya”, Izv. vuzov. Matematika, 1967, no. 1, 3–7 | Zbl

[4] Arestov V.V., “Priblizhenie lineinykh operatorov i rodstvennye ekstremalnye zadachi”, Tr. Matematicheskogo in-ta AN SSSR, 138 (1975), 29–42 | Zbl

[5] Barza S., Burenkov V., Pečarić J., Persson L.-E., “Sharp multidimentional multiplicative inequalities for weighted $L_p$ spaces with homogeneous weights”, Math. Ineq. Appl., 1:1 (1998), 53–67 | DOI | MR | Zbl

[6] Luo M.-J., Raina R.K., “A new extension of Carlson's inequality”, Math. Ineq. Appl., 19:2 (2016), 417–424 | DOI | MR | Zbl

[7] Osipenko K.Yu., “Optimal recovery of operators and multidimensional Carlson type inequalities”, J. Complexity, 32:1 (2016), 53–73 | DOI | MR | Zbl

[8] Osipenko K.Yu., “Inequalities for derivatives with the Fourier transform”, Appl. Comp. Harm. Anal., 53 (2021), 132–150 | DOI | MR | Zbl

[9] Osipenko K.Yu., “Optimal recovery and generalized Carlson inequality for weights with symmetry properties”, [e-resource], 2023, 32 pp., arXiv: https://arxiv.org/pdf/2303.10355.pdf | DOI | MR | Zbl

[10] Osipenko K. Yu., Vypuklyi analiz, URSS, M., 2022, 144 pp.