7 problems

Let $G$ be a Métivier group with sub-Laplacian $\mathcal{L}$, and let $S_*^{\alpha}(\mathcal{L})$ denote the maximal Bochner–Riesz operator associated with $\mathcal{L}$. Write…

Hörmander dichotomy conjecture. The operators $T_\phi^\lambda$ satisfy the operator boundedness estimate for $p>\frac{2n}{n-1}$ if and only if $\phi$ satisfies Bourgain's condition…

Let $d$ be a positive integer, let $m_\delta$ be the Bochner–Riesz multiplier from the classical formulation, and let $\mathfrak{M}_p({\mathbb R}^{2d})$ denote the class of multipl…

Let $\Sigma\subset\mathbb{R}^d$ be a $C^2$ hypersurface with surface measure $\mathrm{d}\sigma$, let $f\in L^2(\Sigma;\mathrm{d}\sigma)$, and let $w$ be a nonnegative weight. Let…

Multiplier conjecture. For $1\leq p\leq\infty$, the estimate

Negative-order Bochner–Riesz conjecture. The operator $\mathcal R^{-\alpha}$ is bounded from $L^p(\mathbb R^d)$ to $L^q(\mathbb R^d)$ if and only if…

Let ${}_{\mathrm{S}^{d-1}}L_p^k$ be the Hardy-type space associated with the unit sphere, and let the Bochner–Riesz operator of order $\lambda>0$ be given as in the source. Bochner…