FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

被引：18

作者：

Gunawan, H. ^{[1
]}

Sawano, Y. ^{[2
]}

Sihwaningrum, I. ^{[1
,3
]}

机构：

[1] Bandung Inst Technol, Dept Math, Bandung 40132, Indonesia

[2] Gakushuin Univ, Dept Math, Toshima Ku, Tokyo 1718588, Japan

[3] Gen Soedirman Univ, Dept Math, Purwokerto 53122, Indonesia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2009年 / 80卷 / 02期

基金：

日本学术振兴会;

关键词：

fractional integral operators; generalized Morrey spaces; nondoubling measures; Olsen's inequality; MORREY SPACES;

D O I：

10.1017/S0004972709000343

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss here the boundedness of the fractional integral operator I-alpha and its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness of I-alpha, we employ the boundedness of the so-called maximal fractional integral operator I-alpha,I-kappa*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

引用

页码：324 / 334

页数：11

共 20 条

[1]

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

[2]

[Anonymous], 2001, Sci. Math. Jpn

[3]

Davies E. B., 1989, CAMBRIDGE TRACTS MAT, V92

[4]

Eridani A., 2004, SCI MATH JPN, V60, P539

[5] Boundedness properties of fractional integral operators associated to non-doubling measures [J].

García-Cuerva, J ;

Gatto, AE .

STUDIA MATHEMATICA, 2004, 162 (03) :245-261

[6]

Gunawan H, 2009, KYUNGPOOK MATH J, V49, P31

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

Hardy, GH ;

Littlewood, JE .

MATHEMATISCHE ZEITSCHRIFT, 1928, 27 :565-606

[8] Some properties of fractional integrals II [J].

Hardy, GH ;

Littlewood, JE .

MATHEMATISCHE ZEITSCHRIFT, 1932, 34 :403-439

[9] Boundedness of integral operators on generalized Morrey spaces and its application to Schrodinger operators [J].

Kurata, K ;

Nishigaki, S ;

Sugano, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (04) :1125-1134

[10]

Nakai E., 2001, Sci. Math. Jpn., V54, P473

← 1 2 →