FRACTIONAL INTEGRAL OPERATOR WITH ROUGH KERNEL ON MORREY SPACES

• Main Author: Salim, Daniel
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/41761
• Institution: Institut Teknologi Bandung

In 1969, Spanne proved boundedness of fractional integral operator T1; in Morrey spaces which are more general than Lebesgue spaces. Adams then proved a stronger result than Spanne’s. Adams inequality is the strongest boundedness property of T1; in Morrey spaces. Meanwhile, Spanne type inequality is the strongest boundedness property of T1; in local Morrey spaces. Morrey spaces is generalized to '-generalized Morrey spaces and -generalized Morrey spaces. In 2009, Guliyev proved boundedness of T1; on '-generalized Morrey spaces. In 2009, Burenkov and Guliyev proved the boundedness of T1; on -generalized Morrey spaces. In this study, we consider fractional integral operator with rough kernel T ;. This operator is a generalization of T1;. We aim to prove boundedness of T ; on Morrey space, local Morrey space, '-generalized Morrey space, and -generalized Morrey space. With restricted domain of T ; to class of radial function, we prove stronger results than Spanne type inequality of T ; on local Morrey spaces. With restricted domain of T ; to some clasess of function, we also prove stronger results than Adams type inequality of T ; on Morrey spaces. In 2014, Iida proved Adams type inequality of T ; on Morrey space. In this dissertation the sufficient condition for boundedness on Iida’s result can be weakened. We also consider vector-valued inequality of maximal operator with rough kernel as the application of boundededness of T ;. Our results generalize Fefferman–Stein’s results which play an important role on atom decomposition theory of Morrey spaces.