Abstract
We introduce a family [Formula: see text] of normal Tricomi domains Ωα,β, α > 0 > β, and we show that its elements are D-star-shaped with respect to the vector field D = -3x∂x- 2y∂yif and only if α ≥ 1/2. Provided that the underlying domain Ω belongs to [Formula: see text] for some α ≥ 1/2, we then establish L2estimates for the eigenfunctions corresponding to real eigenvalues of the Tricomi operator. In particular, our result highlights a dependency of these estimates on the values of α and β and the parabolic diameter of Ω.
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