Related papers: A matrix weighted bilinear Carleson Lemma and Maxi…

We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We study weighted Walsh--Carleson maximal operators arising from dyadic martingale transforms associated with Walsh--Fourier partial sums. For weights satisfying a uniform dyadic variation condition and a uniform bound at the top dyadic…

The famous Carleson-Hunt theorem has been in focus of interest for a long time. This theorem concerns convergence almost everywhere of Fourier series of $f\in L_p$ functions for $1<p\leq \infty.$ Kolmogorov constructed a function $f\in L_1$…

In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and…

The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space.…

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a uniformly rectifiable set of dimension $n$. Then bounded harmonic functions in $\Omega:= \mathbb{R}^{n+1}\setminus E$ satisfy Carleson measure estimates, and are "$\varepsilon$-approximable".…

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

In this paper first we define generalized Carleson mea- sure. Then we consider a special case of it, named conditional Carleson measure on the Bergman spaces. After that we give a characterization of conditional Carleson measures on Bergman…

In this paper we study the double scaling limit of the multi-orientable tensor model. We prove that, contrary to the case of matrix models but similarly to the case of invariant tensor models, the double scaling series are convergent. We…

We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to…

We provide a characterization of Carleson measures on locally finite trees. This characterization establishes the connection between Carleson measures and the boundedness of a suitable Poisson integral between $L^p$-spaces. Additionally,…

In this paper, we prove that all doubling measures on the unit disk $\mathbb{D}$ are Carleson measures for the standard Dirichlet space $\mathcal{D}$. The proof has three ingredients. The first one is a characterization of Carleson measures…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

By $BMO_o(R)$ we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in $BMO_o(R)$ with bounded support as those ones that can be written as a sum of a…

This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbb T$, respectively. For…

For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…

In this paper we study Carleson and reverse Carleson measures on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions in order for a measure $\mu$ to be…

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…

It is well-known that dyadic martingale transforms are a good model for Calder\'on-Zygmund singular integral operators. In this paper we extend some results on weighted norm inequalities to vector-valued functions. We prove that, if $W$ is…