Related papers: $L^2$-estimates for singular oscillatory integral …
In this paper we obtain the non - asymptotic estimations for oscillating integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.
The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces $H^{1}_{+}(w)$ is proved. It is here also show that the…
We study singular integral operators induced by $3$-dimensional Calder\'on-Zygmund kernels in the Heisenberg group. We show that if such an operator is $L^{2}$ bounded on vertical planes, with uniform constants, then it is also $L^{2}$…
For the pair $\{-\Delta, -\Delta-\alpha\delta_\mathcal{C}\}$ of self-adjoint Schr\"{o}dinger operators in $L^2(\mathbb{R}^n)$ a spectral shift function is determined in an explicit form with the help of (energy parameter dependent)…
We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.
We provide $L^1$ estimates for a class of transport equations containing singular integral operators. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is…
For $\alpha, \beta \in L^{\infty} (S^1),$ the singular integral operator $S_{\alpha,\beta}$ on $L^2 (S^1)$ is defined by $S_{\alpha,\beta}f:= \alpha Pf+\beta Qf$, where $P$ denotes the orthogonal projection of $L^2(S^1)$ onto the Hardy…
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…
The eigenvalues of the Liouvillians of Markovian master equation for a harmonic oscillator have a generic form. The Liouvillians considered are quadratic in the position coordinates or creation and annihilation operators, as well as having…
It is known that convergence of l.s.b. closed symmetric sesquilinear forms implies norm resolvent convergence of the associated self-adjoint operators and this in turn convergence of discrete spectra. In this paper in both cases sharp…
We prove an estimate for spherical functions $\varphi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian…
We study the eigenvalues and eigenfunctions of the Folland-Stein operator $\mathscr{L}_\alpha$ on some examples of 3-dimensional Heisenberg Bieberbach manifolds, that is, compact quotients $\Gamma\backslash\mathbb{H}$ of the Heisenberg…
We obtain sharp $L^p$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by…
The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral…
We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
Given $n$ i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form $\Delta_f=\Delta + \alpha \nabla \log f\cdot \nabla$, where $f$ is a positive probability density on a known compact…
We study the perturbed Sobolev space $H^{1,r}_\alpha$, $r \in (1,\infty),$ associated with singular perturbation $\Delta_\alpha$ of Laplace operator in Euclidean space of dimension $2.$ The main results give the possibility to extend the…
This paper is concerned with Schr\"odinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate,…
We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…