Related papers: Existence and smoothness of extremizers for convol…

We give sufficient conditions for compactness of localization operators on modulation spaces $\textbf{M}^{p,q}_{m_{\lambda}}( \mathbb{R}^{d})$ of $\omega$-tempered distributions whose short-time Fourier transform is in the weighted mixed…

We prove that if $\Sigma_{\mathbf A}(\mathbb N)$ is an irreducible Markov shift space over $\mathbb N$ and $f:\Sigma_{\mathbf A}(\mathbb N) \rightarrow \mathbb R$ is coercive with bounded variation then there exists a maximizing probability…

We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to…

We consider convolution equations of the type f * T = g where f, g are in L^p(R^n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T we show that f is compactly supported,…

A necessary and sufficient condition on the precompactness of extremal sequences for one dimensional $\alpha$-Strichartz inequalities, equivalently $\alpha$-Fourier extension estimates, is established based on the profile decomposition…

We find all extremisers for the trace theorem on the sphere. We also provide a sharp extension for functions belonging to certain Sobolev spaces with angular regularity.

A probability-measure-preserving transformation has the Weak Pinsker Property (WPP) if for every $\epsilon>0$ it is measurably conjugate to the direct product of a transformation with entropy $<\epsilon$ and a Bernoulli shift. In a recent…

Let $G$ be a locally compact group and $\mu$ be a measure on $G$. In this paper we find conditions for the convolution operators $\lambda_p(\mu)$, defined on $L^p(G)$ and given by convolution by $\mu$, to be mean ergodic and uniformly mean…

We consider the adjoint restriction inequality associated to the hypersurface $\{(\tau, \xi) : \tau = \pm|\xi|^2, \;\xi \in \mathbb{R}^d\}$ at the Stein-Tomas exponent. Extremizers exist in all dimensions and extremizing sequences are…

We study the generalized existence of extremizers for the sharp $p$-Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean volume growth assumptions. Assuming a nonnegative Ricci…

Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the…

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…

Let $(M,g)$ be a closed Riemannian manifold of dimension $n\geq 3$. If $s$ is a positive integer satisfying $2s<n$, we let $P_g^s$ be the GJMS operator of order $2s$ in $M$. We investigate in this paper the extremal values taken by fixed…

We consider extremal polynomials with respect to a Sobolev-type $p$-norm, with $1<p<\infty$ and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures…

We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…

We obtain new equitightness and $C([0,T];L^p(\mathbb{R}^N))$-convergence results for finite-difference approximations of generalized porous medium equations of the form $$ \partial_tu-\mathfrak{L}[\varphi(u)]=g\qquad\text{in…

In this article, we generalize a theorem of Victor L. Shapiro concerning nontangential convergence of the Poisson integral of a $L^p$-function. We introduce the notion of $\sigma$-points of a locally finite measure and consider a wide class…

We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…

Given a unitary representation U of a compact group G and a transitive G-space $\Omega$, we characterize the extremal elements of the convex set of all U-covariant positive operator valued measures.