Related papers: On maximal functions generated by H\"ormander-type…

Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…

The present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a…

The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…

We analyze spectral properties of the Hilbert $L$-matrix $$\left(\frac{1}{\max(m,n)+\nu}\right)_{m,n=0}^{\infty}$$ regarded as an operator $L_{\nu}$ acting on $\ell^{2}(\mathbb{N}_{0})$, for $\nu\in\mathbb{R}$, $\nu\neq0,-1,-2,\dots$. The…

C. Stockdale, P. Villarroya, and B. Wick introduced the $\epsilon$-maximal operator to prove the Haar multiplier is bounded on the weighted spaces $L^p(w)$ for a class of weights larger than $A_p$. We prove the $\epsilon$-maximal operator…

Consider spherical means on the Heisenberg group with a codimension two incidence relation, and associated spherical local maximal functions $M_Ef$ where the dilations are restricted to a set $E$. We prove $L^p\to L^q$ estimates for these…

Let $L$ be the Dunkl Laplacian on the Euclidean space $\mathbb R^N$ associated with a normalized root $R$ and a multiplicity function $k(\nu)\ge 0, \nu\in R$. In this paper, we first prove that the Besov and Triebel-Lizorkin spaces…

We present an optimization framework based on Lagrange duality and the scattering $\mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection…

We prove that, if \Delta_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-H\"ormander multiplier on the positive half-line, with L^2-order of smoothness greater than…

We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…

In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski…

We prove that wave operators of scattering theory for fourth order Schr\"odinger operators $H = \Delta^2 + V (x)$ on $\mathbb{R}^2$ with real potentials $V(x)$ such that $\langle x \rangle^3 V(x) \in L^{\frac43}(\mathbb{R}^2)$ and $\langle…

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of the bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$…

We prove $L^p\to L^q$ estimates for the local maximal operator associated with dilates of the K\'oranyi sphere in Heisenberg groups. These estimates are sharp up to endpoints and imply new bounds on sparse domination for the corresponding…

In this paper we establish $L^p$ boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein-Uhlenbeck…

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates…

In this paper, we consider the elliptic operators $\mathcal{L}_\varepsilon = -\nabla\cdot (A(X/\varepsilon) \nabla )$ with periodic coefficients in a bounded domain $\Omega$ without any local smoothness assumption on $A = A(Y)$, where…

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds…

We prove $L^p\times L^q\rightarrow L^r$ bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the H\"older relation $1/p+1/q=1/r$. The boundedness region that we get contains at least the interior of…

We prove nontangential and radial maximal function characterizations for Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only…