Related papers: Maximal restriction estimates and the maximal func…
It is well-known that the Fourier extension operator for the paraboloid in $\mathbb{R}^d$ cannot be weak-type bounded at the restriction endpoint $q = 2d/(d-1)$, since such an estimate would imply bounds for the Kakeya maximal function…
Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups. As a corollary, we find that there is no uniform bound on the completely bounded…
For r < 2, we prove the boundedness of a maximal operator formed by applying all multipliers m with $\|m\|_{V^r} \leq 1$ to a given function.
In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy-Littlewood maximal operator associated to certain families of doubling, radial decreasing…
Using variants of the TT* method we give a self-contained proof of the result of Alfonseca, Soria and Vargas on maximal operators on arbitrary directions in $\rr^2$. We also give a sharp $L^2$ estimate for a maximal function extending a…
We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this note, we provide a new maximal…
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…
We estimate in Lp the maximal Riesz transform in terms of the Riesz transform itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is shown to fail. Surprisingly, the weak L1 inequality for the maximal Beurling…
The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case.
We review some results of calculations, having the property of maximal transcendentality.
We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore…
This paper is devoted to study the sharp Moser-Trudinger type inequalities in whole space $\mathbb R^N$, $N \geq 2$ in more general case. We first compute explicitly the \emph{normalized vanishing limit} and the \emph{normalized…
In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the…
Freedman's inequality is a martingale counterpart to Bernstein's inequality. This result shows that the large-deviation behavior of a martingale is controlled by the predictable quadratic variation and a uniform upper bound for the…
Let Mf denote the strong maximal function of f on R^n, that is the maximal average of f with respect to n-dimensional rectangles with sides parallel to the coordinate axes. For any dimension n>1 we prove the natural endpoint Fefferman-Stein…
Among the class of functions with Fourier modes up to degree 30, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality on the circle.
In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.