Matrix parameterized pseudo-differential calculi on modulation spaces

Abstract

We consider a broad matrix parameterized family of pseudo-differential calculi, containing the usual Shubin's family of pseudo-differential calculi, parameterized by real numbers. We show that continuity properties in the framework of modulation space theory, valid for the Shubin's family extend to the broader matrix parameterized family of pseudo-differential calculi.

22 pages. The paper include straight-forward extensions on already well-known results available in papers by Bayer, Cordero, Gröchenig, Heil, Wahlberg and others. In versions 2 and 3: Added one reference, and extended some results to include Lebesgue exponents in the interval (0,\infty ] instead of [1,\infty]. Corrected misprints