K.Yu. Osipenko. Sharp Carlson type inequalities with many weights ... P. 229-240

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, sharp constants

Received June 15, 2023

Revised September 20, 2023

Accepted September 25, 2023

Konstantin Yur’evich Osipenko, Dr. Phys.-Math. Sci., Prof., Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Department of general problems of control, Moscow, 119991, Russia, e-mail: mmmf@mech.math.msu.su; Kharkevich Institute for Information Transmission Problems, Moscow, 127051 Russia, e-mail: director@iitp.ru

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Cite this article as: K.Yu. Osipenko. Sharp Carlson type inequalities with many weights. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, vol. 29, no. 4, pp. 229–240; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2023, Vol. 323, Suppl. 1, pp. S211–S221.