Related papers: Sharp weighted non-tangential maximal estimates vi…

We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the…

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 consider the averages of a function $ f$ on $ \mathbb R ^{n}$ over spheres of radius $ 0< r< \infty $ given by $ A_{r} f (x) = \int_{\mathbb S ^{n-1}} f (x-r y) \; d \sigma (y)$, where $ \sigma $ is the normalized rotation invariant…

We develop the self similarity argument known as sparse domination in an abstract martingale setting, using a continuous time parameter. With this method, we prove a sharp weighted L^p estimate for the maximal operator Y^* of Y with respect…

We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil on…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…

We prove that bilinear forms associated to the rough homogeneous singular integrals $T_\Omega$ on $\mathbb R^d$, where the angular part $\Omega \in L^q (S^{d-1})$ has vanishing average and $1<q\leq \infty$, and to Bochner-Riesz means at the…

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving $L^p$-averages. This class includes the adjoint forms to the bilinear Hilbert…

We prove a local two-weight Poincar\'e inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman--Stein inequality for the sharp maximal…

We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it…

In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions…

In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures.…

Let $r>\frac{4}{3}$ and let $\Omega \in L^{r}(\mathbb{S}^{2n-1})$ have vanishing integral. We show that the bilinear rough singular integral $$T_{\Omega}(f,g)(x)= \textrm{p.v.}…

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…

Doubling metric measure spaces provide a natural framework for singular integral operators. In contrast, the study of maximally modulated singular integral operators, the so-called Carleson operators, has largely been limited to Euclidean…

Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous…

We give a short proof of the sharp weighted bound for sparse operators that holds for all $p$, $1<p<\infty$. By recent developments this implies the bounds hold for any Calder\'on-Zygmund operator. The novelty of our approach is that we…

We introduce a sparse estimation in the ordinary kriging for functional data. The functional kriging predicts a feature given as a function at a location where the data are not observed by a linear combination of data observed at other…

Using tools from semiclassical analysis, we give weighted L^\infty estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provide improved bounds on the number of…

We obtain an improved version of the pointwise sparse domination principle established by the first author in [19]. This allows us to determine nearly minimal assumptions on a singular integral operator $T$ for which it admits a sparse…