FRACTIONAL INTEGRAL OPERATOR ON SMALL MORREY SPACES - Prasetyadi Widyasmara N, Rahmat
Small Morrey space is obtained by choosing specific (t) function on generalized Morrey space Mp (Rn). This thesis will discuss about boundedness of fractional integral operator I on small Morrey spaces mp q (Rn). However, based on Sawano [15], there is another example of (t) function related to small Morrey space that need to be verified. After that, the boundedness of Hardy-Littlewood maximal operator on small Morrey space will be shown. Furthermore, by examining several assumptions of (t) function on boundedness of I in [3] as well as necessary and sufficient condition on boundedness of generalized fractional integral I onMp (Rn) in [2], it will be shown that I is unbounded from m1 p (Rn) to m1 q (Rn).