SOBOLEV'S THEOREM FOR DOUBLE PHASE FUNCTIONALS

被引：25

作者：

Mizuta, Yoshihiro ^{[1
]}

Ohno, Takao ^{[2
]}

Shimomura, Tetsu ^{[3
]}

机构：

[1] 4-13-11 Hachi Hom Matsu Minami, Higashihiroshima 7390144, Japan

[2] Oita Univ, Fac Educ, Dannoharu Oita City 8701192, Japan

[3] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2020年 / 23卷 / 01期

基金：

日本学术振兴会;

关键词：

Riesz potentials; fractional maximal functions; maximal functions; Sobolev's theorem; Musielak-Orlicz spaces; double phase functionals; continuity; VARIABLE EXPONENT; MAXIMAL OPERATOR; REGULARITY; LEBESGUE; SPACES; POTENTIALS; INEQUALITY; EMBEDDINGS;

D O I：

10.7153/mia-2020-23-02

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our aim in this paper is to establish generalizations of Sobolev's theorem for double phase functionals Phi(x,t) =t(p) + {b(x)r(log(e + t))(tau)}(q), where 1 < p <= q < infinity, tau > 0 and b is a nonnegative bounded function satisfying vertical bar b(x) - b(Y)vertical bar <= C vertical bar x - y vertical bar(theta) (log(e + vertical bar x - y vertical bar(-1)))(-tau) for 0 <= theta < 1.

引用

页码：17 / 33

页数：17

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