Related papers: Sharp bounds for $t$-Haar multipliers on $L^2$

For an L ^2-bounded Calderon-Zygmund Operator T, and a weight w \in A_2, the norm of T on L ^2 (w) is dominated by A_2 characteristic of the weight. The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden…

We investigate the unconditional basis property of martingale differences in weighted $L^2$ spaces in the non-homogeneous situation (i.e. when the reference measure is not doubling). Specifically, we prove that finiteness of the quantity…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…

For a matrix A_2 weight W on R^p, we introduce a new notion of W-Calder\'on-Zygmund matrix kernels, following earlier work in by Isralowitz. We state and prove a T1 theorem for such operators and give a representation theorem in terms of…

We obtain a sharp $L^2\times L^2 \to L^1$ boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given function, in terms of the $L^q$ integrability of this…

Using Wilson's Haar basis in $\R^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\R^n$. We can then extend "trivially" Beznosova's Bellman function proof of the linear…

Let $\mathbb{G}$ be a locally compact quantum group with dual $\widehat{\mathbb{G}}$. Suppose that the left Haar weight $\varphi$ and the dual left Haar weight $\widehat{\varphi}$ are tracial, e.g. $\mathbb{G}$ is a unimodular Kac algebra.…

We consider complex projective schemes $X\subset\Bbb{P}^{r}$ defined by quadratic equations and satisfying a technical hypothesis on the fibres of the rational map associated to the linear system of quadrics defining $X$. Our assumption is…

Let $C\subset{\mathbb P}_K^2$ be an algebraic curve over a number field $K$, and denote by $d_K$ the degree of $K$ over ${\mathbb Q}$. We prove that the number of $K$-rational points of height at most $H$ in $C$ is bounded by $c…

We present a number of exact relations for the heavy quark limit and develop an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the new results are relation 3\mu_\pi^2=\bar\Lambda^2 - m_{sp}^2+\beta^2, 1/m_Q…

We present a class of weight functions $ w$ on the circle $ \mathbb{T}$, called L\'evy-Khinchin-Schoenberg (LKS) weights, for which we are able to completely characterize (in terms of a capacitary inequality) all Fourier multipliers for the…

We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w|^2 g for |w| > log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in…

We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving…

The aim of this paper is to study the boundedness of different conical square functions that arise naturally from second order divergence form degenerate elliptic operators. More precisely, let $L_w=w^{-1}\,{\rm div}(w\,A\,\nabla)$ where…

Suppose $((\cdots((x^{2}-c_{1})^{2}-c_{2})^{2}\cdots)^{2}-c_{k-1})^{2}-c_{k}$ splits into linear factors over $\mathbb{Z}$ and $c_{k}\neq0$. We show that for each $j$ and each prime $p$, if $p\leq2^{j-1}$ then $p$ divides $c_{j}$.…

Let $w_{\alpha}(t)=t^{\alpha}\,e^{-t}$, $\alpha>-1$, be the Laguerre weight function, and $|\cdot|_{w_\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\alpha}:=\Big(\int_{0}^{\infty}w_{\alpha}(t)| f(t)|^2\,dt\Big)^{1/2}. $$…

Weprovide an upper bound for generalized Littlewood-Richardson coefficients $c^w_{uv}$, where $u$ is a two-row Young diagram corresponding to a Grassmannian permutation. We end with a conjecture on the upper bounds for all such structure…

Let $w$ be a Muckenhoupt $A_2(\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\mathop\mathrm{div}(A\nabla)$ the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$, $n\geq 2$. In this article, the authors establish some weighted $L^p$…

Quantitative weighted estimates are obtained for the Littlewood-Paley square function $S$ associated with a lacunary decomposition of ${\mathbb R}$ and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence…

Let M denote the maximal function along the polynomial curve p(t)=(t,t^2,...,t^d) in R^d: M(f)=sup_{r>0} (1/2r) \int_{|t|<r} |f(x-p(t))| dt. We show that the L^2-norm of this operator grows at most logarithmically with the parameter d:…