Opérateurs pseudodif[facute]erentiels et classes de gevrey

A calculus approach to hyperfunctions III

“…Then we have Proof of Theorem 2.4. We can obtain merely a weaker conclusion by only the same process of the proof of Theorem 2.3 in case θ > 1 as was seen in a series of papers [5], [16] and [17] which treated the ordinary hypoelliptic problems. However, summing up the method used in the proof of Theorem 2.3 and those of [16], [17] and [24], the proof of the theorem will be accomplished.…”

Partial regularity and applications

“…In Section 2, we prepare some direct extension of the results given in [13] on partial regularity of the distributions and those on pseudodifferential operators given in [7]. In Section 3, we shall establish a method to treat the equations of Grushin type.…”

“…§2. Partial regularity and a class of pseudodifferential operatorsIn this Section, we shall give some refinement of the results in [7] and [13]. Let Ω be an open subset of R N whose point is denoted by x = (x u , x N ).…”

“…We can apply essentially the same method of the proof of [7], Theorem 3.1 and have the relation We note that a function w(x, y) e G^ in a neighborhood of the origin Then we have u e G^ for any solution of (4.3) and u e G%*£%1 for any solution u of (4.4). We remark that relating results have been recently obtained in [15].…”

Gevrey Hypoellipticity for Grushin Operators

“…Therefore, we can apply the Gevrey calculus developed so far for the ordinary pseudodifferential operators, (cf. [12] , [20] , etc.) .…”