Related papers: New bounds for Stein's square function in $\mathbb…

In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two…

Let ${\frak M}^\alpha$ be the spherical maximal operators of complex order $\alpha$ on ${\mathbb R^n}$. In this article we show that when $n\geq 2$, suppose \begin{eqnarray*} \|{\frak M}^{\alpha} f \|_{L^p({\mathbb R^n})} \leq C\|f…

We provide a new direct proof of the $\ell^2$-boundedness of the Discrete Spherical Maximal Function that neither relies on abstract transference theorems (and hence Stein's Spherical Maximal Function Theorem) nor on delicate asymptotics…

This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $\mathbb{R}^d$. We obtain nontangential-maximal-function estimates in $L^p$ and $W^{1, p}$ estimates for $p$ in certain ranges depending…

We reprove Wolff's $L^{\frac{5}2}-$ bound for the $\R^3-$Kakeya maximal function without appealing to the argument of induction on scales. The main ingredient in our proof is an adaptation of Sogge's strategy used in the work on…

Let $ v$ be a smooth vector field on the plane, that is a map from the plane to the unit circle. We study sufficient conditions for the boundedness of the Hilbert transform \operatorname H_{v, \epsilon}f(x) := \text{p.v.}\int_{-\epsilon}^…

It is well known that the Stein-Tomas $L^2$ Fourier restriction theorem can be used to derive sharp $L^p$ bounds for radial Fourier multipliers such as the Bochner-Riesz means. In a similar manner, $L^p \to L^2$ estimates for spectral…

Lebesgue space bounds $L^{p_1}({\mathbb R}^1) \times L^{p_2}(^1) \to L^q({\mathbb R}^1)$ are established for certain maximal bilinear operators. The proof combines a trilinear smoothing inequality with Calder\'on-Zygmund theory. A reference…

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield $2^{\text{nd}}$-order accuracy, the new limiter is…

For a general compact variety $\Gamma$ of arbitrary codimension, one can consider the $L^p$ mapping properties of the B\^ochner-Riesz multiplier $$ m_{\Gamma, \alpha}(\zeta) \ = \ {\rm dist}(\zeta, \Gamma)^{\alpha} \phi(\zeta) $$ where…

We prove $L^p$ lower bounds for Coulomb energy for radially symmetric functions in $\dot H^s(\R^3)$ with $\frac 12 <s<\frac{3}{2}$. In case $\frac 12 <s \leq 1$ we show that the lower bounds are sharp.

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators…

We present new results on the two-weighted boundedness of singular integral operators and $L^p$ boundedness of the Orlicz maximal function. Namely, we extend a theorem of P\'erez regarding the necessary and sufficient conditions for the…

In this paper, we study the boundedness of the Hilbert transformation in Lorentz function spaces, thereby complementing classical results of Boyd. We also characterize the optimal range of a triangular truncation operator in…

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq…

We refine the $L^p$ restriction estimates for Laplace eigenfunctions on a Riemannian surface, originally established by Burq, G\'erard, and Tzvetkov. First, we establish estimates for the restriction of eigenfunctions to arbitrary Borel…

We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard $(p,q)$-growth satisfying the dimension-independent restriction $q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p \leq N-1$,…

In 1997, Thomas Wolff proved sharp $L^3$ bounds for his circular maximal function, and in 1999, Kolasa and Wolff proved certain non-sharp $L^p$ inequalities for a broader class of maximal functions arising from curves of the form…

We investigate the problem of $L^p$-maximal regularity on Banach spaces having a Schauder basis. Our results improve those of a recent paper.

In this paper we establish $L^p$-boundedness properties for variation, oscillation and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.