振荡积分算子及其交换子在加权Morrey空间上的有界性质

Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces

振荡积分算子的有界性质是调和分析研究的中心内容之一.本文得到了由Ricci和Stein定义的一类振荡积分算子在加权Morrey空间中的强型、弱型估计.在此基础上,得到了该类振荡积分算子与BMO函数生成的交换子的强型估计,还建立了分数次振荡积分算子的对应结果.

Boundedness of oscillatory integral operators play a key role in Harmonic Analysis. In this paper, we obtain the strong and weak estimates for a class of oscillatory integral operators, due to Ricci and Stein, on weighted Morrey spaces. Based on the above result, we study the strong boundedness of commutators generated by these oscillatory integral operators and BMO functions. Meanwhile, the corresponding result for the fractional oscillatory integral operators are established.