Related papers: Remark on dyadic pointwise domination and median o…

This article is concerned with finite rank stability theory, and more precisely two classical ways to decompose a type using minimal types. The first is its domination equivalence to a Morley power of minimal types, and the second its…

We prove weighted estimates for rough bilinear singular integral operators with kernel $$K(y_1, y_2) = \frac{\Omega((y_1,y_2)/|(y_1,y_2)|)}{|(y_1, y_2)|^{2d}},$$ where $y_i \in \mathbb{R}^{d}$ and $\Omega \in L^{\infty}(S^{2d-1})$ with…

In this paper we extend dyadic shifts and the dyadic representation theorem to an operator-valued setting: We first define operator-valued dyadic shifts and prove that they are bounded. We then extend the dyadic representation theorem,…

We give again a proof of non-homogeneous T1 theorem. Our proof consists of three main parts: a construction of a random dyadic lattice; an estimate of matrix coefficients of a Calder\'on--Zygmund operator with respect to random Haar basis…

Every submartingale S of class D has a unique Doob-Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0. We provide a short and elementary prove of the Doob-Meyer decomposition theorem.…

We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that…

Following the ideas of Andrei Lerner in [ A pointwise estimate for the local sharp maximal function with applications to singular integrals" Bull. London Math. Soc. 42 (2010) 843856], we obtain another decomposition of an arbitrary…

We in this paper study the nonexpansive operators equipped with arbitrary metric and investigate the connections between firm nonexpansiveness, cocoerciveness and averagedness. The convergence of the associated fixed-point iterations is…

We continue the investigation of abstract Uryson operators in vector lattices. Using the recently proved Up-and-down theorem for order bounded, orthogonally additive operators, we consider the domination problem for AM-compact abstract…

We analyze the pointwise convergence of a sequence of computable elements of L^1(2^omega) in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA_0,…

Let $E \subset \mathbb R^d$, $d \ge 2$, be compact, and let $\phi(x,y)$ be a smooth function satisfying the Phong--Stein rotational curvature condition on $\{\phi(x,y)=1\}$. We prove that if $\dim_{\mathcal H}(E)>1$, then $$…

In this paper we obtain a pointwise sparse domination for generalized H\"ormander operators and also for iterated commutators with those operators. As a particular case of our result we obtain a extension of the sparse domination for…

Due to its nonlocal nature, the $r$-variation norm Carleson operator $C_r$ does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome this difficulty and prove that the dual form to $C_r$ can be…

Let $S$ be the dyadic bi-parameter square function $$Sf(x)^{2} = \sum_{R \in \mathcal{D}} |\langle f, h_{R} \rangle|^{2} \frac{1_{R}(x)}{|R|}.$$ We prove that if $T$ is a bi-parameter martingale transform and $f,g$ are suitable test…

In the uniformly hyperbolic setting it is well known that the set of all measures supported on periodic orbits is dense in the convex space of all invariant measures. In this paper we consider the converse question, in the non-uniformly…

In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…

We consider "Taylor domination" property for an analytic function $f(z)=\sum_{k=0}^{\infty}a_{k}z^{k},$ in the complex disk $D_R$, which is an inequality of the form \[ |a_{k}|R^{k}\leq C\ \max_{i=0,\dots,N}\ |a_{i}|R^{i}, \ k \geq N+1. \]…

We prove a general sparse domination theorem in a space of homogeneous type, in which a vector-valued operator is controlled pointwise by a positive, local expression called a sparse operator. We use the structure of the operator to get…

The technique of sparse domination, i.e., dominating operators with sums of averages taken over sparsely distributed cubes, has seen rapid development recently within the realms of harmonic analysis. A useful extension of sparse domination…

Nous poursuivons l'\'etude d'un contr\^ole \'epars d'un op\'erateur singulier. Plus pr\'ecis\'ement nous expliquons comment on peut conserver certaines propri\'et\'es de l'op\'erateur initial \`a travers un tel contr\^ole et d\'ecrivons…