相关论文: $L^p$-nondegenerate Radon-like operators with vani…

This paper establishes $L^p$-improving estimates for a variety of Radon-like transforms which integrate functions over submanifolds of intermediate dimension. In each case, the results rely on a unique notion of curvature which relates to,…

This paper establishes endpoint $L^p-L^q$ and Sobolev mapping properties of Radon-like operators which satisfy a homogeneity condition (similar to semiquasihomogeneity) and a condition on the rank of a matrix related to rotational…

This paper gives a complete geometric characterization in all dimensions and codimensions of those Radon-like transforms which, up to endpoints, satisfy the largest possible range of local $L^p \rightarrow L^q$ inequalities permitted by…

We prove sharp $L^p$ regularity results for a class of generalized Radon transforms for families of curves in a three-dimensional manifold associated to a canonical relation with fold and blowdown singularities. The proof relies on…

This paper is concerned with establishing uniform weighted $L^p$-$L^q$ estimates for a class of operators generalizing both Radon-like operators and sublevel set operators. Such estimates are shown to hold under general circumstances…

We discuss the closability of directional derivative operators with respect to a general Radon measure $\mu$ on $\mathbb{R}^d$; our main theorem completely characterizes the vectorfields for which the corresponding operator is closable from…

The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…

We show that every point in a uniformly $2$-nondegenerate CR hypersurface is canonically associated with a model $2$-nondegenerate structure. The $2$-nondegenerate models are basic CR invariants playing the same fundamental role as quadrics…

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then…

We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing $L^{2}-$form. Moreover, we prove vanishing theorems…

A nonrigid rotor model is developed from the two-parameter quantum algebra $U_{qp}({\rm u}_2)$. [This model presents the $U_{qp}({\rm u}_2)$ symmetry and shall be referred to as the qp-rotor model.] A rotational energy formula as well as a…

We consider a class of nonlinear non-diagonal elliptic systems with $p$-growth and establish the $L^q$-integrability for all $q\in [p,p+2]$ of any weak solution provided the corresponding right hand side belongs to the corresponding…

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi operator $\Delta_f + |A_f|^2$ has no $L^2$ kernel. In fact, if $\Sigma$ has genus zero and…

In this short note, as a simple application of the strong result proved recently by B\"ohm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of…

Let $M^n$ be a closed manifold of almost nonnegative sectional curvature and nonzero first de Rham cohomology group. For any $[\theta] \in H^1_{dR}(M^n), [\theta] \neq 0$, we show that the Morse- Novikov cohomology group $H^p(M^n, \theta)$…

In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…

We investigate the curvature operator of the second kind on product Riemannian manifolds and obtain some optimal rigidity results. For instance, we prove that the universal cover of an $n$-dimensional non-flat complete locally reducible…

The Radon transform is a bounded operator from $L^p$ of Euclidean space to $L^q$ of the manifold of all affine hyperplanes in $\mathbb{R}^n$ for certain exponents depending dimension. Extremizers have been determined for certain values of…

We show that on conformal manifolds of even dimension $n\geq 4$ there is no conformally invariant natural differential operator between density bundles with leading part a power of the Laplacian $\Delta^{k}$ for $k>n/2$. This shows that a…

Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a cascade of…