RESTRICTION THEOREMS ON WEIGHTED SOBOLEV SPACES OF MIXED NORM

Abstract

By similar methods as Calderón [1] and Stein [10], we prove some restriction theorems on weighted potential spaces when the weight satisfies Muckenhoupt’s $A_p$ condition. We then construct potential spaces of mixed norm and find that mixed norm potential spaces are indeed a natural object in the study of restriction theorems. With the help of mixed norm spaces, we obtain a better version of restriction theorem.