BOUNDEDNESS OF INTEGRAL OPERATORS ON MORREY SPACES - SUFYAN (NIM: 20116010), ABU
This thesis studies about the boundedness of some integral operators on Morrey spaces, where the Morrey space M_q^p (R^n ) is defined as the set of all measurable functions f that satisfy ‖f‖_(M_q^p )=sup┬(a∈R^n,r>0)⁡〖|B(a,r)|^(1/q-1/p) 〗 [∫_B(a,r)▒〖|f(y)|^p dy〗]^(1/p)<∞. Some operators whose boundedness on Morrey spaces M_q^p (R^n ) are studied are Hardy-Littlewood maximal function M, fractional integral operators I_α, and fractional maximal functions M_α. We also study about the relationship between the norm of fractional integral operators I_α and the norm of fractional maximal operators M_α on Lebesgue spaces and Morrey spaces.