Global analytic and Gevrey surjectivity of the Mizohata operator \( D_2 + i x^{2k}_{2} D_{1} \)

Cattabriga, Lamberto ; Zanghirati, Luisa

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 1, pp. 37-39.

Abstract (VO)

The surjectivity of the operator \( D_2 + i x^{2k}_{2} D_{1} \) from the Gevrey space \( \mathcal{E}^{\{s\}}(\mathbb{R}^{2}) \), \( s \geq 1 \), onto itself and its non-surjectivity from \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \) to \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \) is proved.

Riassunto

Si prova che l'operatore \( D_2 + i x^{2k}_{2} D_{1} \) è suriettivo dallo spazio di Gevrey \( \mathcal{E}^{\{s\}}(\mathbb{R}^{2}) \), \( s \geq 1 \), su sé stesso e che ciò non accade per lo stesso operatore da \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \) ad \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \).

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