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FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

Published online by Cambridge University Press:  29 June 2009

H. GUNAWAN*
Affiliation:
Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia (email: [email protected])
Y. SAWANO
Affiliation:
Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan (email: [email protected])
I. SIHWANINGRUM
Affiliation:
Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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