Related papers: Extremisers for the trace theorem on the sphere

In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents…

We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with colinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing…

The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal…

We prove the existence of functions that extremize the endpoint $L^2$ to $L^4$ adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space $\mathbb{R}^4$ and that, taking symmetries into consideration, any…

In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces…

We show that, under certain regularity assumptions, there exists a linear extension operator.

We survey a few trace theorems for Sobolev spaces on $N$-dimensional Euclidean domains. We include known results on linear subspaces, in particular hyperspaces, and smooth boundaries, as well as less known results for Lipschitz boundaries,…

We prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces. This provides a positive solution to…

We prove trace and extension results for Sobolev-type function spaces that are well suited for nonlocal Dirichlet and Neumann problems including those for the fractional $p$-Laplacian. Our results are robust with respect to the order of…

We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in…

The Tomas-Stein inequality or the adjoint Fourier restriction inequality for the sphere $S^1$ states that the mapping $f\mapsto \hat{f\sigma}$ is bounded from $L^2(S^1)$ to $L^6(\mathbb{R}^2)$. We prove that there exists an extremizer for…

In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.

We show explicit forms for extremals of some fourth-order sharp trace inequalities on the unit balls recently proved by Ache-Chang. We also give a classification result of the bi-harmonic equation on $\mathbb{R}^4_+$ with some conformally…

In this article, we develop a linear profile decomposition for the $L^p \to L^q$ adjoint Fourier restriction operator associated to the sphere, valid for exponent pairs $p<q$ for which this operator is bounded. Such theorems are new when $p…

We study the Sobolev trace constant for functions defined in a bounded domain $\O$ that vanish in the subset $A.$ We find a formula for the first variation of the Sobolev trace with respect to hole. As a consequence of this formula, we…

In this paper, we consider the trace theorem for modulation spaces, alpha modulation spaces and Besov spaces. For the modulation space, we obtain the sharp results.

We provide sharp forms of $k$-plane transform inequalities on the $d$-dimensional sphere $\mathbb{S}^d$ and the $d$-dimensional hyperbolic space $\mathbb{H}^d$. In particular, we prove that extremizers do not exist for $\mathbb{H}^d$. This…