Related papers: Estimates for compositions of maximal operators wi…

In this paper, we consider the Lam\'e operator $-\Delta^\ast$ and study resolvent estimate, uniform Sobolev estimate, and Carleman estimate for $-\Delta^\ast$. First, we obtain sharp $L^p$--$L^q$ resolvent estimates for $-\Delta^\ast$ for…

It is well known that the weak ($1,1$) bounds doesn't hold for the strong maximal operators, but it still enjoys certain weak $L\log L$ type norm inequality. Let $\Phi_n(t)=t(1+(\log^+t)^{n-1})$ and the space $L_{\Phi_n}({\mathbb R^{n}})$…

In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum…

Consider a normal Ornstein--Uhlenbeck semigroup in $\Bbb{R}^n$, whose covariance is given by a positive definite matrix. The drift matrix is assumed to have eigenvalues only in the left half-plane. We prove that the associated maximal…

Lacey and Thiele have recently obtained a new proof of Carleson's theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher…

In this manuscript we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of discrete Fourier multipliers (Fourier multipliers on $\mathbb{Z}^n$). Our main goal is to apply the results…

We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in…

We obtain some estimates for norm and essential norm of the difference of two composition operators between weighted Bergman spaces $A^p_\alpha$ and $A^q_\beta$ on the unit ball. In particular, we completely characterize the boundedness and…

We give new lower bounds for $L^p$ estimates of the Schr\"odinger maximal function by generalizing an example of Bourgain.

We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.

This paper comprises two parts. In the first, we study $L^p$ to $L^q$ bounds for spectral multipliers and Bochner-Riesz means with negative index in the general setting of abstract self-adjoint operators. In the second we obtain the uniform…

In this paper we establish maximum principles for weakly 1-coercive operators $L$ on complete, non-compact Riemannian manifolds $M$. In particular, we search for conditions under which one can guarantee that solutions $u$ of differential…

In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on $A_{\alpha}^{2}$ with symbols…

We explore some variants of the Boman covering lemma, and their relationship to the boundedness properties of the maximal operator. Let $1 < p < \infty$ and let $q$ be its conjugate exponent. We prove that the strong type $(q,q)$ of the…

We prove L2 x L2 to weak L1 estimates for some novel bilinear maximal operators of Kakeya and lacunary type thus extending to this setting, the works of Cordoba and of Nagel, Stein and Wainger.

We give criteria for weak and strong invariant closed sets for differential inclusions given in $\mathbb{R}^{n}$ and governed by Lipschitz Cusco perturbations of maximal monotone operators. Correspondingly, we provide different…

Let $(X, d, \mu)$ be a space of homogeneous type and $\Omega$ an open subset of $X$. Given a bounded operator $T: L^p(\Omega) \to L^q(\Omega)$ for some $1 \le p \le q < \infty$, we give a criterion for $T$ to be of weak type $(p_0, a)$ for…

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…

We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are…

The goal of this paper is to provide a new approach to address the $L^p-$boundedness of bilinear rough singular integral operators. This approach relies on local Fourier series expansion of input functions leading to trilinear estimates…