CRITERIA FOR EMBEDDING OF GENERALIZED BESSEL AND RIESZ POTENTIAL SPACES IN REARRANGEMENT INVARIANT SPACES

被引：4

作者：

Bokayev, N. A. ^{[1
]}

Goldman, M. L. ^{[2
]}

Karshygina, G. Zh. ^{[1
]}

机构：

[1] LN Gumilyov Eurasian Natl Univ, Dept Mech & Math, 5 Munaitpasov St, Nur Sultan 010008, Kazakhstan

[2] RUDN Univ, Peoples Friendship Univ Russia, Inst Math, 6 Mikluho Maklaya St, Moscow 117198, Russia

来源：

EURASIAN MATHEMATICAL JOURNAL | 2019年 / 10卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

functional norm; cones of functions with monotonicity conditions; embedding of potential spaces in rearrangement-invariant spaces; generalized Bessel and Riesz potentials; CONES;

D O I：

10.32523/2077-9879-2019-10-2-08-29

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the spaces of generalized Bessel and Riesz potentials and establish criteria for the embedding of these spaces in rearrangements invariant spaces. To do this we obtain constructive equivalent descriptions for the cones of decreasing rearrangement of potentials. Covering and equivalence of cones are studied with respect to order relations which allows to weaken substantially the assumptions on the kernels of potentials.

引用

页码：8 / 29

页数：22

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