Nikolai Dokuchaev
The paper studies completeness of the polynomials in weighted $L_p$-spaces on half line. It is shown that the completeness of polynomials does not hold for a wide class of weights, including the weights $\exp(- r t^q)$ with $r>0$ and $q\in (0,1)$.
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Spectrum of Hausdorff operators on weighted Bergman and Hardy spaces of the upper half-plane
本文研究了上半平面加权伯格曼和幂加权硬叶空间上豪斯多夫算子的谱特性。
We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operators satisfy relaxed Dini conditions. We apply the weighted estimates to extrapolation of maximal $L^p$ regularity of first order, second order and fractional order Cauchy problems into weighted rearrangement invariant Banach function spaces. In particular, we provide extensions, as well as a unification of recent results due to Auscher and Axelsson,…
We prove some weighted $L_p$ estimates for generalized harmonic extensions in the half-space.
Some equivalent definitions for weighted Korenblum and Bloch-type spaces of the upper half-plane
本文通过有界Hankel算子的符号，证明了上半平面加权Korenblum空间和Bloch型空间的等价刻画。
Sharp weighted non-tangential maximal estimates via Carleson-sparse domination
本文利用伴随奇异积分的逐点稀疏控制，证明了将函数从$\mathbf{R}^n$映射到上半空间的奇异积分非切向极大函数的尖锐加权估计，并用Carleson平均值替代通常平均值建立了非标准稀疏控制。
We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.
Boundedness of the Bergman projection on some weighted mixed norm Lebesgue spaces of the upper-half space
本文证明了上半空间加权混合范数空间上 Bergman 投影的有界性，其充要条件仅依赖参数，并给出了对偶、导数表征及原子分解等应用。
We consider the linear span S of the functions tak (with some ak > 0) in weighted L2 spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comparisons are also made between the new results and those that can be deduced from older ones in the literature.
Conjectures of Bernstein and Erd\H os for weighted Lagrange interpolation on the halfline with exponential weights
本文证明了半直线上带指数权的加权拉格朗日插值算子的Bernstein和Erdős猜想，首次处理了导数矩阵奇异的情况。
We study properties of $W_0^{1,p}(\mathbb{R}_+,t^β)$ - the completion of $C_0^\infty(\mathbb{R}_+)$ in the power-weighted Sobolev spaces $W^{1,p}(\mathbb{R}_+,t^β)$, where $β\in\mathbb{R}$. Among other results, we obtain the analytic characterization of $W_0^{1,p}(\mathbb{R}_+,t^β)$ for all $β\in \mathbb{R}$. Our analysis is based on the precise study the two trace operators: $Tr^{0}(u):= \lim_{t\to 0} u(t)$ and $Tr^{\infty}(u):= \lim_{t\to \infty} u(t)$, which leads to the analysis of the asymptotic behavior of functions from $W_0^{1,p}(\mathbb{R}_+,t^β)$ near zero or infinity. The obtained s…
On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights
本文研究带指数权重半轴和赫尔米特权重全轴插值中非奇异性的有效性，发现导数矩阵可能奇异，并探讨伯恩斯坦和埃德罗斯猜想的延续性。
Rellich type inequalities on the half line in the framework of equalities
本文在等式框架下建立了半直线上的加权Hardy和Rellich型不等式，推广了近期相关结果，并证明了一维经典Rellich不等式在等式框架下成立。
We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.
We study the asymptotics near the origin of the Fourier transform in weighted Hardy spaces of analytic functions in the upper half-plane, and of the Laplace transform in weighted spaces of entire functions of zero exponential type. These results are applied to two closely related problems posed by E. Dyn'kin: we find the asymptotics of the depth of zero in non-quasianalytic Denjoy-Carleman classes, and of the exact Levinson-Sjoberg majorant.
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal operators satisfy strong and weak type inequalities. Our characterizations are in terms of Sawyer and Békollé-Bonami type conditions. We also obtain a $Φ$-bump characterization for these maximal functions, where $Φ$ is a Orlicz function. As a consequence, we obtain two-weight norm inequalities for fractional Bergman operators. Finally, we provide some sharp weighted…
Dispersive Decay Estimates for periodic Jacobi operators on the half-line
该研究针对离散半直线上的周期Jacobi算子，推导了不同条件下的色散时间衰减速率，完善了相关算子的色散衰减理论。
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