相关论文: Sharp Maximal function estimates for Multilinear p…

In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the…

For any nonempty set $U\subset\R^+$, we consider the maximal operator $\h^U$ defined as $\h^Uf=\sup_{u\in U}|H^{(u)} f|$, where $H^{(u)}$ represents the Hilbert transform along the monomial curve $u\gamma(s)$. We focus on the…

Multiparameter maximal estimates are considered for operators of Schr\"odinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which…

In this paper, we establish dimension-free estimates for the discrete spherical maximal operator on semi-commutative $L_{p}$ space for $2\leq p\leq\infty$.

In this article we develop a functional model for a general maximal dissipative operator. We construct the selfadjoint dilation of such operators. Unlike previous functional models, our model is given explicitly in terms of parameters of…

For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…

In this work we show endpoint boundedness properties of pseudo-differential operators of type $(\rho,\rho)$, $0<\rho<1$, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols.

For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight estimates of mixed type in the two-weight and…

We prove a dispersive estimate for periodic discrete Schr\"odinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schr\"odinger equation with…

In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…

In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We obtain sharp estimates for the localized distribution function of M\phi, when \phi belongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…

In this work we establish sharp boundedness results for pseudo-differential operators corresponding to $a\in\mathcal{S}_{0,0}^{m}$ on Triebel-Lizorkin spaces $F_p^{s,q}$ and Besov spaces $B_p^{s,q}$.

This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with symbols in the H\"ormander classes. Here we prove pointwise…

We obtain an asymptotic formula for the counting function of the discrete spectrum for Hankel-type pseudo-differential operators with discontinuous symbols.

The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish…

Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…

In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which…