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:

Necessary and Sufficient Conditions for the Boundedness of Fractional Integral Operators on Hypergroups

Author(s):

Ari Wardayani, Mutia Nur Estri, Wihantoro, Idha Sihwaningrum

Faculty of Mathematics and Natural Sciences,
Jenderal Soedirman University,
Indonesia.
E-mail: ari.wardayani@unsoed.ac.id
mutia.estri@unsoed.ac.id
wihantoro@unsoed.ac.id
idha.sihwaningrum@unsoed.ac.id

Abstract:

We prove in this paper the necessary and sufficient conditions for the boundedness of the fractional integral operators on Lebesgue spaces over commutative hypergroups. The necessity proofs take into account the Haar measure, meanwhile the sufficiency proofs employ the maximal operators.

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