Abstract
We investigate various G type spaces on Rd+ and their relations with the Gelfand-Shilov S type spaces on R2d through the mapping w : R2d ? Rd+, w(x, ?) = (2x21 + 2?21 ,..., 2x2d + 2?2d ). Sufficient conditions for the hypoellipticity of symbols originating from the coordinante radial symbols in G type spaces are also given. Two open problems explained in the introduction are posed.
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