Morrey spaces and weighted norm inequalities

本文研究了Morrey空间框架下的多线性分数阶积分算子和多（次）线性分数阶极大算子的权重理论。给出了这些算子的一权不等式和二权不等式的自然充分条件，并由此导出了多线性分数阶积分算子的Olsen不等式。研究了Morrey空间框架中势型积分算子的局部迹不等式，给出了势型积分算子具有局部有限非负Borel测度的范数不等式成立的充分条件。给出了Hardy-Littlewood极大算子在Morrey空间上双权范数不等式成立的充分必要条件。并验证了功率权重的充要条件。

In this research, a theory of weights for multilinear fractional integral operators and multi(sub)linear fractional maximal operators in the framework of Morrey spaces is developed. Natural sufficient conditions for the one and two weight inequalities of these operators are given, and, as a corollary, the Olsen inequality for multilinear fractional integral operators is obtained.The local trace inequality for potential type integral operators in the framework of Morrey spaces is studied and the sufficient conditions for the norm inequality with a locally finite nonnegative Borel measure of potential type integral operators to hold are given. Necessary condition and sufficient condition for two-weight norm inequalities on Morrey spaces to hold are given for the Hardy-Littlewood maximal operator.Necessary and sufficient condition is also verified for the power weights.