Related papers: Point evaluation in Paley--Wiener spaces

Recent work [BGS17,ABGS19] has shown SETH hardness of CVP in the $\ell_p$ norm for any $p$ that is not an even integer. This result was shown by giving a Karp reduction from $k$-SAT on $n$ variables to CVP on a lattice of rank $n$. In this…

We study the parabolic fractional $p-$Laplace equation $$\p_t u+(-\Delta_p)^su = 0$$ in the degenerate range \(2 \leq p < 2/(1-s)\). We show that weak solutions are Lipschitz continuous in space and, if \(p > 1/(1-s)\), also in time. We…

Dependencies of the optimal constants in strong and weak type bounds will be studied between maximal functions corresponding to the Hardy--Littlewood averaging operators over convex symmetric bodies acting on $\mathbb R^d$ and $\mathbb…

Given a real-valued weighted function $f$ on a finite dag, the $L_p$ isotonic regression of $f$, $p \in [0,\infty]$, is unique except when $p \in [0,1] \cup \{\infty\}$. We are interested in determining a ``best'' isotonic regression for $p…

Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods…

We establish interior $C^{1,\alpha}$ regularity estimates for some $\alpha > 0$, for solutions of the fractional $p$-Laplace equation $(-\Delta_p)^s u = 0$ when $p$ is in the range $p \in [2,2/(1-s))$.

The projection constant $\Pi(E):=\Pi(E, \ell_\infty)$ of a finite-dimensional Banach space $E\subset\ell_\infty$ is by definition the smallest norm of a linear projection of $\ell_\infty$ onto $E$. Fix $n\geq 1$ and denote by $\Pi_n$ the…

This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and…

We study Birkhoff-James orthogonality and its pointwise symmetry in commutative $C^*$ algebras, i.e., the space of all continuous functions defined on a locally compact Hausdorff space that vanish at infinity. We use this characterization…

Let $Z=(Z_t)_{t\geq0}$ be an additive process with a bounded triplet $(0,0,\Lambda_t)_{t\geq0}$. Suppose that for any Schwartz function $\varphi$ on $\mathbb{R}^d$ whose Fourier transform is in $C_c^{\infty}(B_{c_s} \setminus B_{c_s^{-1}}…

In this paper we consider an abstract Wiener space $(X,\gamma,H)$ and an open subset $O\subseteq X$ which satisfies suitable assumptions. For every $p\in(1,+\infty)$ we define the Sobolev space $W_{0}^{1,p}(O,\gamma)$ as the closure of…

Using upper $\ell_p$-estimates for normalized weakly null sequence images, we describe a new family of operator ideals $\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$ and $1\leq\xi\leq\omega_1$. These classes…

The best constant and extremal functions are well known of the following Caffarelli-Kohn-Nirenberg inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p\frac{\mathrm{d}x}{|x|^{\mu}}\geq \mathcal{S}…

Let $m,n\in\mathbb{N}$ and $p\in(0,\infty)$. For a finite dimensional quasi-normed space $X=(\mathbb{R}^m, \|\cdot\|_X)$, let $$B_p^n(X) = \Big\{ (x_1,\ldots,x_n)\in\big(\mathbb{R}^{m}\big)^n: \ \sum_{i=1}^n \|x_i\|_X^p \leq 1\Big\}.$$ We…

In this paper we prove a partial $C^{1,\alpha}$ regularity result in dimension $N=2$ for the optimal $p$-compliance problem, extending for $p\not = 2$ some of the results obtained by A. Chambolle, J. Lamboley, A. Lemenant, E. Stepanov…

For an operator T from X to Y denote m(T) the infimum of $||Tx||$ on the unit sphere $S_X$ of X. A sequence $(x_n)$ in $S_X$ is said to be minimizing for T if $||Tx_n||$ tends to m(T). In 2020 U. S. Chakraborty introduced and studied the…

This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…

Let \(P_+\) be the Riesz's projection operator and let \(P_-=I-P_+.\) We find the best upper estimates of the expression \(\left\lVert \left( \left\lvert P_+f \right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} \right\rVert _p…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

We use the formalism of the R{\'e}nyi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal functions we mean functions which realize the equality…