Affiliation:
1. School of Mathematics Sun Yat‐sen University Guangzhou Guangdong China
2. Department of Mathematics The Ohio State University Columbus Ohio USA
Abstract
AbstractModified from the standard half‐space extension via the reflection principle, we construct a linear extension operator for the upper half space that has the form for . We prove thatEis bounded in all ‐spaces, Sobolev and Hölder spaces, Besov and Triebel–Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains.
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