Related papers: Bounds for anisotropic Carleson operators

We consider Schr\"odinger operators at a fixed high frequency on simply connected compact Riemannian manifolds with non-positive sectional curvatures and smooth strictly convex boundaries. We prove that the Dirichlet-to-Neumann map uniquely…

We construct a class of Fourier multipliers whose associated operators are weak (1,1) bounded but fail to be weak (p, p) bounded for any 1 < p \leq \infty. Moreover, we show that this result is sharp.

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…

In this paper we prove that the Hardy-Littlewood maximal operator is bounded on Morrey spaces $\mathcal{M}_{1,\lambda}(\rn)$, $0 \le \la < n$ for radial, decreasing functions on $\rn$

We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…

We extend an estimate of Taibleson and Weiss, regarding Fourier transform of Hardy spaces, to the aniostropic setting. As consequences, we obtain necessary conditions for multiplier operators, and the anisotropic version of the…

In [24, Theorem 2'] Charles Fefferman has proved the weak (1,1) boundedness for a class of oscillating singular integrals that includes the oscillating spectral multipliers of the Euclidean Laplacian $\Delta,$ namely, operators of the form…

We prove that the lacunary Carleson operator is bounded from $L \log L$ to $L^{1}$. This result is sharp. The proof is based on two newly introduced concepts: 1) the \emph{time-frequency regularization of a measurable set} and 2) the…

We obtain the partial-wave unitarity constraints on the lowest-dimension effective operators which generate anomalous quartic gauge couplings but leave the triple gauge couplings unaffected. We consider operator expansions with linear and…

In this paper we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the ellipsoid. We show that the general method of the thin shell…

We prove the boundedness of the maximal operator and Hilbert transform along certain variable parabolas in $L^p$ for $p>p_0$ with some $p_0\in (1, 2)$. Connections with the Hilbert transform along vector fields and the polynomial Carleson's…

Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex…

We prove an extension of the Walsh-analog of the Carleson-Hunt theorem, where the $L^\infty$ norm defining the Carleson maximal operator has been replaced by an $L^q$ maximal-multiplier-norm. Additionally, we consider certain associated…

We study the weighted boundedness of the Cauchy singular integral operator $S_\Gm$ in Morrey spaces $L^{p,\lambda}(\Gm)$ on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted…

We study the Carleson measures on NTA and ADP domains in the Heisenberg groups $\mathbb{H}^n$ and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the…

We give a function F(d,n,p) such that if K/Q_p is a degree n field extension and A/K is a d-dimensional abelian variety with potentially good reduction, then #A(K)[tors] is at most F(d,n,p). Separate attention is given to the prime-to-p…

Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, with $L^p$-boundary data for $p$ near $2$ (more precisely, in…

In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our…

In this paper we obtain the sharp quantitative matrix weighted weak type bounds for the Christ--Goldberg maximal operator $M_{W,p}$ in the case $1<p<2$, improving a recent result by Cruz-Uribe and Sweeting. Also, in the scalar setting, we…

In this work, we prove limitations on the known methods for designing matrix multiplication algorithms. Alman and Vassilevska Williams recently defined the Universal Method, which substantially generalizes all the known approaches including…