Boundedness of Stein Weiss Operator on Several Classical Spaces
Sofihara Al Hazmy1, Al Azhary Masta2, Siti Fatimah3

1Faculty of Military Mathematics and Science, Universitas Pertahanan Republik Indonesia, Kawasan IPSC Sentul, Sukahati, Bogor, Jawa Barat 16810

2,3 Department of Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi 229, Bandung 40154, Indonesia

Abstract

In 1958, Stein-Weiss have been provided necessary and sufficient condition for boundedness of Stein-Weiss operator on Lebesgue space. But there are several generalizations of Lebesgue space, for example Orlicz and Morrey space. Our curiosity lead us to seek some necessary and sufficient conditions for the boundedness of Stein-Weiss Operator on Orlicz and Morrey Spaces. We have found several results and will be provided in this presentation.
The results on Orlicz space and Morrey space will be provided separately. In particular, on the Morrey space, we have two types of boundedness, which will be known as Spanne and Adams type.

Keywords: Orlicz spaces, Fractional Integral, Stein-Weiss Operator, Boundedness

Topic: Mathematics