相关论文: Sharp $L^1$ estimates for singular transport equat…
We obtain the estimate of the Lebesgue measure of the spectrum for the direct integral of matrix-valued functions. These estimates are applicable for a wide class of discrete periodic operators. For example: these results give new and sharp…
We prove square function estimates in $L_2$ for general operators of the form $B_1D_1+D_2B_2$, where $D_i$ are partially elliptic constant coefficient homogeneous first order self-adjoint differential operators with orthogonal ranges, and…
The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for…
In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and L1 and L2 energy for drifting heat equation on closed manifolds with weighted measure. In some sense, this study is about the eigenvalue…
We investigate possible quantifications of strictly singular operators, $l_{p}$-strictly singular operators, $c_{0}$-strictly singular operators, strictly cosingular operators, $l_{p}$-strictly cosingular operators. We prove quantitative,…
In the first part of the paper we continue the study of solutions to Schr\"odinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schr\"odinger operator involves a…
Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.
We obtain spectral estimates for the iterations of Ruelle operator $L_{f + (a + \i b)\tau + (c + \i d) g}$ with two complex parameters and H\"{o}lder functions $f,\: g$ generalizing the case $\Pr(f) =0$ studied in [PeS2]. As an application…
In this paper, we consider a kind of singular integral which can be viewed as an extension of the classical Calder$\acute{\rm o}$n-Zygmund type singular integral. We establish an estimate of the singular integral in the $L^q$ space for…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
In this paper it is proposed a very simple method for estimating the maximal operator in $L_1$. Using this method one can considerably improve the existing theorems on convergence almost-everywhere of eigenfunction expansions of an…
We study generalized solutions of multidimensional transport equation with bounded measurable solenoidal field of coefficients $a(x)$. It is shown that any generalized solution satisfies the renormalization property if and only if the…
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…
We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…
In this manuscript, we provide local $L^q$-estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimates are used to establish uniform large-scale $L^q$-estimates…
Two-side estimates for two-weighted discrete Hardy-type operators on a tree are obtained. For general weights we prove the discrete analogue of Evans - Harris - Pick theorem (it is a quite simple consequence from their result). It gives the…