Related papers: Dyadic harmonic analysis and weighted inequalities…
This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the id\`ele class space, we place a…
In this paper, we characterize the sharp constant and maximizing functions for weighted Poincar\'e inequalities. These results lead to refinements of Hardy's inequality obtained by adding remainder terms involving \(L^p\) norms. We use…
We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated…
For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of…
This paper studies Difference-in-Differences (DiD) setups with repeated cross-sectional data and potential compositional changes across time periods. We begin our analysis by deriving the efficient influence function and the semiparametric…
We give an alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables, is possible. This last…
Motivated by the work of Cheng-Fang-Wang-Yu on the hypersingular Bergman projection, we develop a real-variable framework for hypersingular operators in regimes where strong-type bounds fail on the critical line. Our main new ingredient is…
We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differential-algebraic equations (DAEs). We establish asymptotic…
The vector-valued $T(1)$ theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a…
We give again (see also arXiv:1112.0676) a proof of weighted estimate of any Calder\'on-Zygmund operator. This is under a universal sharp sufficient condition that is weaker than the so-called bump condition. Bump conjecture was recently…
Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators,…
We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…
In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…
This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of…
A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a…
We introduce the use of harmonic analysis to decompose the state space of symmetric robotic systems into orthogonal isotypic subspaces. These are lower-dimensional spaces that capture distinct, symmetric, and synergistic motions. For linear…
In this paper we study harmonic analysis operators in Dunkl settings associated with finite reflection groups on Euclidean spaces. We consider maximal operators, Littlewood-Paley functions, $\rho$-variation and oscillation operators…
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the…
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 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…