No, it is not the mark of Pieter I van Somerwil.

Fake mark of the Amsterdam silversmith Pieter I van Somerwil, registered in Amsterdam, 1706-died 1753. Pseudo Amsterdam town mark.
Again this is Pieter van Somerwil I his mark;
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Peter.
Source; K. A. Citroen, Valse Zilvermerken in Nederland #428 and # 526