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FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

Part of: Higher-dimensional theory Integral, integro-differential, and pseudodifferential operators Real functions Harmonic analysis in several variables

Published online by Cambridge University Press:  29 June 2009

H. GUNAWAN ,
Y. SAWANO  and
I. SIHWANINGRUM
H. GUNAWAN*
Affiliation:
Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia (email: hgunawan@math.itb.ac.id)
Y. SAWANO
Affiliation:
Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan (email: yosihiro@math.gakushuin.ac.jp)
I. SIHWANINGRUM
Affiliation:
Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia (email: hanidha@students.itb.ac.id)
*
✉For correspondence; e-mail: hgunawan@math.itb.ac.id
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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.

Keywords

fractional integral operatorsgeneralized Morrey spacesnondoubling measuresOlsen’s inequality

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 47G10: Integral operators 31B10: Integral representations, integral operators, integral equations methods 26A33: Fractional derivatives and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 324 - 334
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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