Original Article
Kyungpook Mathematical Journal 2009; 49(1): 31-39
Published online March 23, 2009
Copyright © Kyungpook Mathematical Journal.
Fractional Integrals and Generalized Olsen Inequalities
Hendra Gunawan1, Eridani2
1Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
2Department of Mathematics, Airlangga University Surabaya 60115, Indonesia
Let $T_ho$ be the generalized fractional integral operator associated to a function $ho:(0,infty) o(0,infty)$, as defined in cite{Nak2}. For a function $W$ on $n$, we shall be interested in the boundedness of the multiplication operator $fmapsto W cdot T_ho f$ on generalized Morrey spaces. Under some assumptions on $ho$, we obtain an inequality for $W cdot T_ho$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.
Keywords: Fractional integral operators, Hardy-Littlewood maximal operators, multiplication operators, Olsen inequality, Morrey spaces