Violo, Ivan Yuri (2017) Extension operators on Sobolev-Morrey spaces. [Magistrali biennali]
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In the present work we will prove that also the Hestenes extension operator and the Stein extension operator have the property of preserving Sobolev-Morrey spaces. In particular we will prove two main results, Theorem 2 and Theorem 7, which respectively prove inequality (1) when T is taken to be the Hestenes and the Stein operator. We also point out that the proof of Theorem 7 will differ considerably from the proof of the corresponding result in , which was based on the \local nature" of the Burenkov extension operator. Since the Stein operator have a somewhat more \global nature" and rigid structure, we will have to develop a different approach.
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