Related papers: On two weight estimates for dyadic operators

We prove a pointwise estimate for positive dyadic shifts of complexity $m$ which is linear in the complexity. This can be used to give a pointwise estimate for Calder\'on-Zygmund operators and to answer a question posed by A. Lerner.…

We prove $L^{p}$ and weighted $L^{p}$ estimates for bounded functions of a selfadjoint operator satisfying both a pointwise gaussian estimate for its heat kernel and a finite speed of propagation property. As an application, we obtain…

In this paper, we study tractability of $L_2$-approximation of one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are of product form. For the algorithms we allow information from the class…

In this paper we establish square-function estimates on the double and single layer potentials for divergence-form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This…

We consider a two weight $L^{p}(\mu) \to L^{q}(\nu)$-inequality for well localized operators as defined and studied by F. Nazarov, S. Treil and A. Volberg when $p=q=2$. A counterexample of F. Nazarov shows that the direct analogue of these…

Lacey and Thiele have recently obtained a new proof of Carleson's theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher…

We study multivariate $L_2$-approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences…

Following the ideas of A. Lerner, F. Nazarov, S. Ombrosi from [12] we prove that there is a sequence of weights $w\in A^d_1$ such that $[w]^d_{A_1}\to \infty$, and martingale transforms $T$ such that with an absolute positive $c$ $\|T:…

We provide quantitative weighted estimates for the $L^p(w)$ norm of a maximal operator associated to cube skeletons in $\mathbb{R}^n$. The method of proof differs from the usual in the area of weighted inequalities since there are no…

We build up a quantitative second order Sobolev estimate of $ \ln w$ for positive $p$-harmonic functions $w$ in Riemannian manifolds under Ricci curvature bounded from blow and also for positive weighted $p$-harmonic functions $w$ in…

We define a time faithful dyadic shift operator of complexity one, that is an antisymmetric antiinvolution. We show that the Hilbert transform with values in a Banach space is $L^p$ bounded if and only if the dyadic shift is -- with a…

We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding…

In this paper, starting with a relatively simple observation that the variational estimates of the commutators of the standard Calder\'on-Zygmund operators with the BMO functions can be deduced from the weighted variational estimates of the…

In this paper, we provide necessary and sufficient conditions on a triple of weights $(u,v,w)$ so that the $t$-Haar multipliers $T^t_{w,\sigma}$, $t\in \R$, %defined in \cite{P} when $\sigma=1$, are uniformly (on the choice of signs…

We prove that the operator norm on weighted Lebesgue space L2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2-characteristic of the weight, as opposed to the linear…

We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.

Let $R$ be the vector of Riesz transforms on $\mathbb{R}^n$, and let $\mu,\lambda \in A_p$ be two weights on $\mathbb{R}^n$, $1 < p < \infty$. The two-weight norm inequality for the commutator $[b, R] : L^p(\mathbb{R}^n;\mu) \to…

In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators $T_b^m$. Our results are new even for the first order commutator $T_b^1$. A new bump type…

The $X^{s,b}$ spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain…

We extend the recently much-studied two-weight commutator estimates to the multilinear setting. In contrast to previous results, our result respects the multilinear nature of the problem fully and is formulated with the genuinely…