Paper's Title:

The boundedness of Bessel-Riesz operators on generalized Morrey spaces

Author(s):

Mochammad Idris, Hendra Gunawan and Eridani

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: mochidris@students.itb.ac.id

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
E-mail: eridani.dinadewi@gmail.com

Abstract:

In this paper, we prove the boundedness of Bessel-Riesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedberg-type inequality for the operators, and the boundedness of Hardy-Littlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.

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:

Some Inequalities for the Generalized Riesz Potential on the Generalized Morrey Spaces over Hypergroups

Author(s):

I. Sihwaningrum, Renny, Y. Dasril

Jenderal Soedirman University,
Indonesia.
E-mail: idha.sihwaningrum@unsoed.ac.id renny@unsoed.ac.id
 

Universiti Tun Hussein Onn,
Malaysia.
E-mail: yosza@uthm.edu.my

Abstract:

We present in this paper some inequalities for the generalized Riesz potential on the generalized Morrey spaces over commutative hypergroups. The results can be found by employing the maximal operator.

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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