相关论文: Estimation of weighted $L^2$ norm related to Demai…

In this article, we establish a support function of the weighted $L^2$ integrations on the superlevel sets of the weights with optimal asymptoticity near the positive infinity, which is an analogue of the truth of Demailly's strong openness…

Generalized Lelong numbers of plurisubharmonic functions with respect to plurisubharmonic weights (due to Demailly) are specified for weights with multicircled asymptotics. Explicit formulas for these values are obtained in terms of the…

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

In this article, we give a proof of the strong openness conjecture for plurisubharmonic functions posed by Demailly.

We give a proof of the openness conjecture of Demailly and Koll\'ar for positively curved singular metrics on ample line bundles over projective varieties. As a corollary it follows that the openness conjecture for plurisubharmonic…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…

Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…

We prove the sharp mixed norm $(l^2, L^{q}_{t}L^{r}_{x})$ decoupling estimate for the paraboloid in $d + 1$ dimensions.

We give a proof of the openness conjecture of Demailly and Koll\'ar.

We reduce the Openness Conjecture of Demailly and Koll\'ar on the singularities of plurisubharmonic functions to a purely algebraic statement.

We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…

We prove the matrix $A_2$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear dependence on the matrix $A_2$ constant in the estimate. Moreover,…

In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic…

Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying $\mathrm{Ric}_{\infty} \ge 1$, we give an $L^1$-estimate exhibiting that the push-forward of the reference measure by the guiding function (arising from the…

In this paper we consider weighted $L^2$ integrability for solutions of the wave equation. For this, we obtain some weighed $L^2$ estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of…

We establish a new class of $L^2$-weighted elliptic estimates on smooth two-manifolds for a family of weights satisfying an equation with explicit constants. This family includes weights that are comparable to the product of positive powers…

Using Bellman function approach, we present new proofs of weighted $L^2$ inequalities for square functions, with the optimal dependence on the $A_2$ characteristics of the weight and further explicit constants. We study the estimates both…

We show that valuations on the ring R of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions, giving rise to generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic function thus…

In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the…

We consider here a problem of finding the sharp estimate for the boundedness of an arbitrary Calder\'on-Zygmund operator in $L^2(w)$, $w\in A_2$. We first prove that for $A_2$ weight $w$ one has that the norm a Calderon--Zygmund operator…