Abstract
We consider the Bochner-Riesz means for the Hermite and special Hermite expansions. Developing further Thangavelu's approach [31], we study their Lp boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of p and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the Lp summability index for the Hermite Bochner-Riesz means in Rd, d≥2. This invalidates the conventional conjecture which was expected to be true.
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