Near optimal $$L^p\rightarrow L^q$$ estimates for euclidean averages over prototypical hypersurfaces in $$\mathbb {R}^3$$
Mathematische Annalen - Trang 1-56 - 2024
Tóm tắt
We find the precise range of (p, q) for which local averages along graphs of a class of two-variable polynomials in
$$\mathbb {R}^3$$
are of restricted weak type (p, q), with hypersurfaces equipped with Euclidean surface measure. We derive these results using non-oscillatory, geometric methods, for a model class of polynomials bearing a strong connection to the general real-analytic case.
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