Related papers: On pointwise estimates involving sparse operators

We prove Calder\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of…

In this paper we characterize BMO in terms of the boundedness of commutators of various bilinear singular integral operators with pointwise multiplication. In particular, we study commutators of a wide class of bilinear operators of…

A simple shortcut to proving sharp weighted estimates for the Martingale Transform and for the dyadic shift of order 1 (and so for the Hilbert transform) is presented. It is a unified proof for these both transforms. Key words:…

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…

In connection with proving the A_2 conjecture in 2010, T. Hyt\"onen obtained a representation of general Cald\'eron-Zygmund operators in terms of simpler operators known as Haar shifts. In this note, we prove that the result is sharp in the…

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative…

Let $T$ be a Calder\'on-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions on the weight…

This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calder\'on-Zygmund operators in R^n such that the maximal singular integral can be controlled in the L^2 norm by the singular integral.…

We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard $\alpha$-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions.…

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As a direct application…

The following subexponential estimate for commutators is proved |[|\{x\in Q: |[b,T]f(x)|>tM^2f(x)\}|\leq c\,e^{-\sqrt{\alpha\, t\|b\|_{BMO}}}\, |Q|, \qquad t>0.\] where $c$ and $\alpha$ are absolute constants, $T$ is a Calder\'on--Zygmund…

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

We discuss boundedness properties of certain classes of discrete bilinear operators that are similar to those of the continuous bilinear pseudodifferential operators with symbols in the H\"ormander classes $BS^{\omega}_{1, 0}$. In…

In this paper, we establish jump and variational inequalities for the Calder\'{o}n commutators, which are typical examples of non-convolution Calder\'on-Zygmund operators. For this purpose, we also show jump and variational inequalities for…

In this paper, we establish a new characterization of weighted $\rm{VMO}$ spaces, which are essential different from the classical $\rm{VMO}$ spaces, via the compactness of sparse operators, commutators of Riesz potentials and fractional…

In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

We prove a quadratic sparse domination result for general non-integral square functions $S$. That is, we prove an estimate of the form \begin{equation*} \int_{M} (S f)^{2} g \, \mathrm{d}\mu \le c \sum_{P \in \mathcal{S}}…

In this note the weak type estimates for fractional integrals are studied. More precisely, we adapt the arguments of Domingo-Salazar, Lacey, and Rey to obtain improvements for the endpoint weak type estimates for regular fractional sparse…