Related papers: Three examples of Sharp Commutator Estimates via H…
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
This master thesis is based on the paper "Sharp commutator estimates via harmonic extensions" by Lenzmann and Schikorra, in which they proposed a method to prove estimates for commutators involving Riesz transforms, fractional Laplacians…
In this paper we extend a Calderon-Zygmund commutator-type estimate. This estimate enables us to prove an embedding result concerning weighted function spaces.
Sharp weighted estimates are obtained for vector-valued extensions of the Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators and Coifman-Rochberg-Weiss commutator. Those estimates will rely upon suitable pointwise estimates in…
We give a general method to obtain from the integral restrictions of functions sharp pointwise and uniform estimates of these functions. This scheme is illustrated by the examples for Fock\,--\,Bargmann spaces of entire functions of several…
In this paper quantitative weighted matrix estimates for vector valued extensions of $L^{r'}$-H\"ormander operators and rough singular integrals are studied. Strong type $(p,p)$ estimates, endpoint estimates, and some new results on…
We prove a functional inequality in any dimension controlling the derivative along a transport of the Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by the third author and collaborators…
In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\'{o}n-Zygmund operators, multilinear…
We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super-Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by…
We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is…
A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…
We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate…
We give coefficient estimates for a class of close-to-convex harmonic mappings, and discuss the Fekete-Szeg\H{o} problem of it. We also introduce two classes of polyharmonic mappings $\mathcal{HS}_{p}$ and $\mathcal{HC}_{p}$, consider the…
We prove sharp interpolatory estimates between Riesz Transforms and directional Haar projections. We obtain applications to the theory of compensated compactness and prove a conjecture of L. Tartar on semi-continuity of separately convex…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick…
Kink model is developed to analyze the data where the regression function is twostage linear but intersects at an unknown threshold. In quantile regression with longitudinal data, previous work assumed that the unknown threshold parameters…
In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel.…
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal…
The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular model for count data due to its ability to capture both under dispersion and over dispersion. However, CMP regression is limited when dealing with complex nonlinear…