In the context of manifolds of bounded geometry, we show that the properties of proper uniform pseudo-differential operators (PUPDOs) constructed by Kordyukov, Meladze, and Shubin carry over to PUPDOs whose local representations have symbols belonging to the (weighted) class \(M_{\rho ,\varLambda }^{m}\) introduced by Garello and Morando. Under the M-ellipticity assumption, we show that the minimal and maximal extensions of such PUPDOs in the \(L^p\)-spaces, where \(1<p<\infty \), coincide.

中文翻译：

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非紧流形上$$ L ^ p $$ L p空间中M-次椭圆适当一致伪微分算子的最小和最大扩展

在有界几何流形的上下文中，我们证明了由Kordyukov，Meladze和Shubin构造的适当的统一伪微分算子（PUPDO）的性质会延续到PUPDO，其局部表示具有属于（加权）类\（由Garello和Morando引入的M _ {\ rho，\ varLambda} ^ {m} \）。在M椭圆度假设下，我们证明\（L ^ p \）-空间中此类PUPDO的最小和最大扩展是重合的，其中\（1 <p <\ infty \）是重合的。