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This talk is based on a series of papers jointed with Professor Jie Xiao at Memorial University. Starting from Adams' restricting principles for Riesz-Lebesgue potentials, we will talk about restricting principles for Riesz-Morrey, Riesz-Hardy-Morrey, Riesz-Lorentz-Morrey & Riesz-Besov potentials, as well as their applications in some fractional partial differential equations.