Related papers: $Tb$ theorem on product spaces

We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers in the spaces $L_{p,Y}(\mathbb T^d)$ are equivalent for all…

In this brief note we provide a simple approach to give a new proof of the well known fact that the Banach-Alaoglu theorem and the Tychonoff product theorem for compact Hausdorff spaces are equivalent.

Schoenberg showed that a function $f:(-1,1)\rightarrow \mathbb{R}$ such that $C=[c_{ij}]_{i,j}$ positive semi-definite implies that $f(C)=[f(c_{ij})]_{i,j}$ is also positive semi-definite must be analytic and have Taylor series coefficients…

We prove that in the Laver model for the consistency of the Borel's conjecture, the product of any two $H$-separable spaces is $M$-separable.

We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function…

It is solved the problem on constructed of separately continuous functions on product of two topological spaces with given restriction. In particular, it is shown that for every topological space $X$ and first Baire class function $g:X\to…

We prove several results on products of conjugacy classes in finite simple groups. The first result is that there always exists a uniform generating triple. This result and other ideas are used to solve a 1966 conjecture of Peter Neumann…

We revisit the work of Bourgain, Kahn, Kalai, Katznelson and Linial (1992) -- referred to as ``BKKKL'' in the title -- about influences on Boolean functions in order to give a precise statement of threshold phenomenon on the product space…

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of…

We prove a quantitative version of Hilbert's irreducibility theorem for function fields: If $f(T_1,\ldots, T_n,X)$ is an irreducible polynomial over the field of rational functions over a finite field $\mathbb{F}_q$ of characteristic $p$,…

We continue developing the theory of conical and vertical square functions on $R^{n}$, where $\mu$ is a power bounded measure, possibly non-doubling. We provide new boundedness criteria and construct various counterexamples. First, we prove…

We prove a Green--Tao theorem for multiplicative functions.

Local $Tb$ theorems with $L^p$ type testing conditions, which are not scale invariant, have been studied widely in the case of the Lebesgue measure. Until very recently, local $Tb$ theorems in the non-homogeneous case had only been proved…

We define as a distribution the product of a function (or distribution) h in some Hardy space Hp with a function b in the dual space of Hp. Moreover, we prove that the product bxh may be written as the sum of an integrable function with a…

Let $p(\cdot):\mathbb R^n\rightarrow(0,\infty)$ be a variable exponent function satisfying the globally log-H\"older continuous condition. In this paper, we obtain the boundedness of para-product operators $\pi_b$ on variable Hardy spaces…

Let $X$ be the product of a surface satisfying $b_2=\rho$ and of a curve over a finite field. We study a strong form of the integral Tate conjecture for $1$-cycles on $X$. We generalize and give unconditional proofs of several results of…

For a bounded singular integral $T_n$ in $\mathbb{R}^n$ and a bounded singular integral $T_m$ in $\mathbb{R}^m$ we prove that $$ \| [T_n^1, [b, T_m^2]] \|_{L^p(\mu) \to L^p(\lambda)} \lesssim_{[\mu]_{A_p}, [\lambda]_{A_p}}…

We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is…

We study thermal two-point functions and four-point functions involving two heavy twisted operators and two light probes in symmetric product orbifolds. We identify cases where they are universal at large $N$, that is, they are only…

This article begins the theory of submanifolds into products of 2 or more space forms. The tensors $\mathbf{R}$, $\mathbf{S}$ and $\mathbf{T}$ defined by Lira, Tojeiro and Vit\'orio at \cite{LTV} and the Bonnet theorem proved by them are…