相关论文: $L^p$-$L^q$ boundedness of integral operators with…

$(L_p, L_q)$ estimates are obtained for oscillatory potentials $(K^\alphaf)(x)=\int\limits_{R^n}\frac{\exp(i|y|)}{|y|^{n-\alpha}}f(x-y)dy$, $0<\alpha<n$, $n\geq 2$, whose symbol has a singularity on the unit sphere. These potentials are…

In the paper, we provide a new method to study the oscillatory singular integral operator $T_{Q,A}$ with nonstandard kernel defined by \[T_{Q,A} f(x)=\text { p.v. } \int_{\mathbb{R}^{n}} f(y)…

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…

In the paper, we study a kind of Oscillatory singular integral operator with Calder\'{o}n Type Commutators $T_{P,K,A} $ defined by \[T_{P,K,A} f(x)=\text { p.v.} \int_{\mathbb{R}^{n}} f(y) \frac{K(x-y)}{|x-y|}(A(x)-A(y)-\nabla A(y))(x-y)…

In the paper, we consider integral operators with non-negative kernels satisfying conditions, which are less restrictive than conditions studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.

Consider the operator $ T=-{d^2dx^2}+x^2+q(x)$ in $L^2(\mathbb{R})$, where real functions $q$, $q'$ and $\int_0^xq(s)ds$ are bounded. In particular, $q$ is periodic or almost periodic. The spectrum of $T$ is purely discrete and consists of…

Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…

In this paper, we establish the global boundedness of oscillatory integral operators on Besov-Lipschitz and Triebel-Lizorkin spaces, with amplitudes in general $S^m_{\rho,\delta}(\mathbb{R}^n)$-classes and non-degenerate phase functions in…

We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but…

We obtain two-weighted $L^2$ norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and…

In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…

In this paper we study the $L^p$-$L^q$ boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator $A$. Using the notion of a…

For every $\alpha \in (0,+\infty)$ and $p,q \in (1,+\infty)$ let $T_\alpha$ be the operator $L^p[0,1]\to L^q[0,1]$ defined via the equality $(T_\alpha f)(x) := \int_0^{x^\alpha} f(y) d y$. We study the norms of $T_\alpha$ for every $p$,…

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|^{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators…

We study the asymptotic behaviour of a finite network of oscillators (harmonic or anharmonic) coupled to a number of deterministic Lagrangian thermostats of finite energy. In particular, we consider a chain of oscillators interacting with…

Let $\nu$ be a positive measure on $[0,1]$. A Shimorin-type operator $T_\nu$ is an integral operator on the unit disk given by \[ T_\nu f(z) = \int_{\mathbb{D}} \frac{1}{1 - z\overline{\lambda}} \left( \int_0^1 \frac{d\nu(r)}{1 - r z…

We find a minimal notion of non-degeneracy for bilinear singular integral operators $T$ and identify testing conditions on the multiplying function $b$ that characterize the $L^p\times L^q\to L^r,$ $1<p,q<\infty$ and $r>\frac{1}{2},$…

In this paper, we shall prove the $L^{p}$ endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases $S$ in $\mathbb{R} \times \mathbb{R}$. As a consequence, sharp $L^{p}$ decay estimates are also obtained…

Oscillatory integral operators with $1$-homogeneous phase functions satisfying a convexity condition are considered. For these we show the $L^p - L^p$-estimates for the Fourier extension operator of the cone due to Ou--Wang via polynomial…