Boundedness of certain oscillatory integrals on weighted L(p) spaces and some results on weighted weak H(p) 0 <= p <= 1.

摘要

In this thesis, we provide a necessary and sufficient condition for Lp boundedness of a class of oscillatory integrals with Calderon-Zygmund (C-Z) Kernel and establish weighted norm inequalities for them. We also prove some weighted norm inequalities for a class of oscillatory integrals with rough kernel. Finally, we discuss the question of the sharpness of certain weighted weak type inequalities for standard C-Z operators.