Related papers: Sharp Fourier extension for functions with localiz…

We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for…

We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schr\"odinger equation. In this work, we establish the existence…

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.

In this paper we show a new inequality which generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second…

We prove a sharp Beckner's inequality for axially symmetric functions on $S^4$. The key ingredients of our proof is some pointwise quantitative properties of Gegenbauer polynomials.

Let $Z$ be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on $Z$ which parallels the work of Harish-Chandra. The constant terms $f_I$ of an eigenfunction $f$ are parametrized by subsets $I$…

We study the quantitative stability associated with the adjoint Fourier restriction inequality, focusing on the paraboloid and two-dimensional sphere cases. We show that these Strichartz-stability inequalities admit minimizers attaining…

Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between…

Sharp Fourier restriction theory and finite field extension theory have both been topics of interest in the last decades. Very recently, in \cite{GonzalezOliveira}, the research into the intersection of these two topics started. There it…

We provide several asymptotic expansions of the prime counting function $\pi(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a possibly…

We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of…

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…

Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…

We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is…

Building on the classical work of C\'{o}rdoba--Fefferman and the recent work of Schippa, we establish $L^4$ reverse square function estimates for functions whose Fourier support is contained in a $\delta$-neighborhood of the curve…

We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\u{\i} spaces on the whole $\mathbb{R}^N$. By generalizing a recent work by Hynd and Seuffert, we prove existence of extremals, together with some…

In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel.…

Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type…

In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…

We prove that the improved Moser-Trudinger inequality with optimal coefficient $\alpha =1/2$ holds for all functions on $S^2$ with zero moments.