On the boundedness of the integral convolution operator in a pair of classical Lebesgue spaces Lp and Lr

被引：0
|
作者：
Pavlov, Evgeniy A. [1 ]
Furmenko, Aleksandr I. [2 ,3 ]
机构：
[1] Crimean State Engn Pedag Univ, Dept Math, Simferopol, Ukraine
[2] NE Zhukovsky & YA Gagarin Air Force Acad, Phys & Math, Voronezh, Russia
[3] NE Zhukovsky & YA Gagarin Air Force Acad, Dept Math, Voronezh, Russia
来源：
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS | 2023年 / 83期
关键词：
integral convolution operator; boundedness; boundedness criterion; Lebesgue spaces;
D O I：
10.17223/19988621/83/5
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
In this paper, in terms of the kernel K(t) of the integral convolution operator, a constructive criterion for its boundedness in a pair of classical Lebesgue spaces L-p and L-r is obtained. It is shown that the integral convolution operator acts boundedly from L-p into L-r,(p) if and only if the kernel K(t) belongs to the Marcinkiewicz space M t(1-1/q) .
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页码：52 / 58
页数：7
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