Related papers: Operator-valued dyadic harmonic analysis beyond do…

Concerned with elliptic operators with stationary random coefficients governed by linear or nonlinear mixing conditions and bounded (or unbounded) $C^1$ domains, this paper mainly studies (weighted) annealed Calder\'on-Zygmund estimates,…

This is an expository paper on the helicoidal method, a tool designed for proving multiple vector-valued inequalities for operators in harmonic analysis, which is based on stopping times and localizations. As it turns out, the local…

We constructively determine the Pietsch measure of the 2-summing multiplication operator \[\mathcal{M}_u:\ell^{\infty} \rightarrow H^p, \quad (\varphi_I) \mapsto \sum \varphi_Ix_Ih_I. \] Our construction of the Pietsch measure for the…

We study Borel systems and continuous systems of measures, with a focus on mapping properties: compositions, liftings, fibred products and disintegration. Parts of the theory we develop can be derived from known work in the literature, and…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

For arbitrarily small values of $\varepsilon>0,$ we formulate and analyse the Maxwell system of equations of electromagnetism on $\varepsilon$-periodic sets $S^\varepsilon\subset{\mathbb R}^3.$ Assuming that a family of Borel measures…

Let $T$ be a multilinear Calder\'on-Zygmund operator of type $\omega$ with $\omega(t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{\Pi\vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The…

We introduce the so called convex body valued sparse operators, which generalize the notion of sparse operators to the case of spaces of vector valued functions. We prove that Calder\'on--Zygmund operators as well as Haar shifts and…

In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative $L_{p}$-spaces. The main result is a weak $(1,1)$ type estimate of this square function. We also show the $(L_{\infty},\mathrm{BMO})$…

In this paper, a weak type (1,1) bound criterion is established for singular integral operator with rough kernel. As some applications of this criterion, we prove some important operators with rough kernel in harmonic analysis, such as…

Standard interpolating operators for charged mesons, e.g. $J_{B} = \bar b i \gamma_5 u$ for $B^-$, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by…

In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the…

Let $\mu$ be a non-negative Borel measure on $R^d$ satisfying that the measure of a cube in $R^d$ is smaller than the length of its side raised to the $n$-th power, $0<n\leq d$. In this article we study the class of weights related to the…

We address the generalized measurement of the two-boson operator $Z_\gamma= a_1 + \gamma a_2^\dag$ which, for $|\gamma|^2 \neq 1$, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly…

We prove that the operator norm on weighted Lebesgue space L2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2-characteristic of the weight, as opposed to the linear…

We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients of the proof are regularity estimates for convolution of…

Let $\sigma:\boldsymbol{\Sigma}\to\boldsymbol{\Sigma}$ be the left shift acting on $ \boldsymbol{\Sigma} $, a one-sided Markov subshift on a countable alphabet. Our intention is to guarantee the existence of $\sigma$-invariant Borel…

This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…

We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…

In this paper we investigate weighted composition operators between weak and strong vector valued weighted Bergman spaces and Hardy spaces.