Related papers: A polynomial Carleson operator along the paraboloi…
We study some complete orthonormal systems on the real-line. These systems are determined by Bargmann-type transforms, which are Fourier integral operators with complex-valued quadratic phase functions. Each system consists of…
We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of…
In this paper we present a unified approach to the spectral analysis of an hypergeometric type operator whose eigenfunctions include the classical orthogonal polynomials. We write the eigenfunctions of this operator by means of a new Taylor…
A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a…
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…
This thesis is devoted to asymptotic norm estimates for oscillatory integral operators acting on the L^2 space of functions of one real variable. The operators in question have compact support and an oscillatory kernel of the form exp(i…
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the…
The first three results in this thesis are motivated by a far-reaching conjecture on boundedness of singular Brascamp-Lieb forms. Firstly, we improve over the trivial estimate for their truncations, thus excluding potential trivial…
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…
We develop several Euclidean operator radius bounds for the product of two $d$-tuple operators using positivity criteria of a $2\times 2$ block matrix whose entries are $d$-tuple operators. From these bounds, by using the polar…
Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this article we develop a novel framework for these square…
The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calder\'on's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing…
The Malmquist-Takenaka system is a perturbation of the classical trigonometric system, where powers of $z$ are replaced by products of other M\"obius transforms of the disc. The system is also inherently connected to the so-called nonlinear…
We study an elliptic operator $L:=\mathrm{div}(A\nabla \cdot)$ on the upper half plane $\mathbb{R}^2_+$. There are several conditions on the behavior of the matrix $A$ in the transversal $t$-direction that yield $\omega\in…
In one-sided Chord-Arc Domains $\Omega$, we demonstrate that the $A_\infty$-absolute continuity of the elliptic measure with respect to the surface measure remains stable under $L^2$ Carleson perturbations. This stability holds provided…
We explore baryon-number-violating ($|\Delta B| = 2$) processes beyond the well-known neutron-antineutron ($n - \bar{n}$) oscillations, focusing on the $\Lambda - \bar \Lambda$ system. The presence of a strange quark in the $\Lambda$ baryon…
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 consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\times \mathbb R\times \mathbb R:\ x_{n+1}>0\}$, $n\geq 1$. We…
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…
The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of…