


Paper's Title:
Fractional Integral Operators and Olsen Inequalities on NonHomogeneous Spaces
Author(s):
Idha Sihwaningrum, Herry P. Suryawan, Hendra Gunawan
Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia
hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
We prove the boundedness of the fractional integral operator I_{α} on generalized Morrey spaces of nonhomogeneous type. In addition, we also present Olsentype inequalities for a multiplication operator involving I_{α}. Our proof uses a result of GarcíaCuerva and Martell [3].
Paper's Title:
Weak Type Inequalities for Some Operators on Generalized Morrey Spaces Over Metric Measure Spaces
Author(s):
Idha Sihwaningrum, Ari Wardayani, Hendra Gunawan
Faculty of Mathematics and Natural
Sciences,
Jenderal Soedirman University, Purwokerto 53122,
Indonesia.
Email: idha.sihwaningrum@unsoed.ac.id
ariwardayani@yahoo.co.id
Faculty of Mathematics and Natural
Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
Email: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
We discuss weak type inequalities for maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces. Here the measure satisfies the so called growth condition. By taking into account the maximal operator, we obtain a Hedberg type inequality, which leads us to the weak type inequality for the fractional integral operator on the same spaces.
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