Related papers: The Carleson Embedding Theorem with matrix weights
We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…
The extension of the Campbell-Magaard embedding theorem to general relativity with minimally-coupled scalar fields is formulated and proven. The result is applied to the case of a self-interacting scalar field for which new embeddings are…
We strengthen the Carleson-Hunt theorem by proving $L^p$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $p>\max\{r',2\}$. Four appendices are concerned with transference, a variation norm…
In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a…
Assuming the bilinear reverse Holder's condition, we character weighted inequalities for the bilinear maximal operator on filtered measure spaces. We also obtain Hytonen-Perez type weighted estimates for the bilinear maximal operator. Our…
We prove a version of Carleson's Theorem in the Walsh model for vector-valued functions: For $1<p< \infty$, and a UMD space $Y$, the Walsh-Fourier series of $f \in L ^{p}(0,1;Y)$ converges pointwise, provided that $Y$ is a complex…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and…
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator…
We prove a local $Tb$ theorem for paraproducts acting on vector valued functions, with matrix weighted averaging operators. The condition on the weight is that its square is in the $L_2$ associated matrix $A_\infty$ class. We also introduce…
We obtain characterizations of positive Borel measures $\mu$ on $\B^n$ so that some weighted holomorphic Besov spaces $B_s^p(w)$ are imbedded in $L^p(d\mu)$, where $w$ is a $B_p$ weight in the unit ball of $\C^n$.
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
Coifman--Meyer multipliers represent a very important class of bi-linear singular operators, which were extensively studied and generalized. They have a natural multi-parameter counterpart. Decomposition of those operators into…
We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskii-LaSalle invariance principle to the case of general…
In this paper, using a generalization of a Richter and Sundberg representation theorem, we give a new characterization of Carleson measures for the Dirichlet-type space $\mathcal D(\mu)$ when $\mu$ is a finite sum of point masses. A…
Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson…
In this paper we prove two matrix weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a matrix symbol. More precisely, we extend the recent results of the second author, Pott, and Treil on…
In this paper, we establish an anisotropic version of Campanato Theorem and show that the anisotropic Bessel spaces are continuously embedded in the spaces of Holder continuous functions. As an application of this embedding, we build…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
We first extend Calder\'on's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.