Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

被引：45

作者：

Mizuta, Yoshihiro ^{[2
]}

Nakai, Eiichi ^{[3
]}

Ohno, Takao ^{[1
]}

Shimomura, Tetsu ^{[4
]}

机构：

[1] Hiroshima Natl Coll Maritime Technol, Higashino Oosakikamijima 7250231, Japan

[2] Hiroshima Univ, Fac Integrated Arts & Sci, Div Math & Informat Sci, Higashihiroshima 7398521, Japan

[3] Osaka Kyoiku Univ, Dept Math, Osaka 5828582, Japan

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

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2011年 / 56卷 / 7-9期

关键词：

Morrey spaces of variable exponent; Riesz potentials; Sobolev embeddings; Sobolev's inequality; Trudinger's exponential inequality; Lipschitz spaces of variable exponent; CONTINUITY PROPERTIES; INTEGRAL-OPERATORS; MAXIMAL OPERATOR;

D O I：

10.1080/17476933.2010.504837

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let alpha, nu, beta, p and q be variable exponents. Our aim in this article is to deal with Sobolev embeddings for Riesz potentials of order alpha with functions f in Morrey spaces L-Phi,L-nu,L-beta(G) with Phi(t) = t(p)(log(e + t))(q) over a bounded open set G subset of R-n. Here p and q satisfy the log-Holder and the loglog-Holder conditions, respectively. Also the case when p attains the value 1 in some parts of the domain is included in our results.

引用

页码：671 / 695

页数：25

共 29 条

[1]

Adams D. R., 1996, Function Spaces and Potential Theory

[2]

ADAMS DR, 1975, DUKE MATH J, V42, P765, DOI 10.1215/S0012-7094-75-04265-9

[3]

Almeida A, 2008, GEORGIAN MATH J, V15, P195

[4]

[Anonymous], 2008, Banach and Function Spaces II

[5]

[Anonymous], 2004, BANACH FUNCTION SPAC

[6]

[Anonymous], 1965, Ann. Scuola Norm. Sup. Pisa

[7]

[Anonymous], 1989, GRADUATE TEXTS MATH

[8]

Chiarenza F., 1987, Rend. Mat., V7, P273

[9]

Cruz-Uribe D, 2009, T AM MATH SOC, V361, P2631

[10] Some properties of fractional integrals I [J].

Hardy, GH ;

Littlewood, JE .

MATHEMATISCHE ZEITSCHRIFT, 1928, 27 :565-606

← 1 2 3 →