Paper's Title:

Fractional Integral Operators and Olsen Inequalities on Non-Homogeneous 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 non-homogeneous type. In addition, we also present Olsen-type inequalities for a multiplication operator involving I_α. Our proof uses a result of García-Cuerva 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.
E-mail: idha.sihwaningrum@unsoed.ac.id ariwardayani@yahoo.co.id

Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: 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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