相关论文: $L^p$-estimates of extensions of holomorphic funct…

We prove L^1 --> L^\infty estimates for the linear Schroedinger equation in three dimensions. The potential is assumed to belong to certain L^p spaces, but no pointwise decay estimates and no additional regularity is required.

All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.

We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of…

In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of…

An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive…

An example is given of a hyperconvex manifold without non-constant bounded holomorphic functions, which is realized as a domain with real-analytic Levi-flat boundary in a projective surface.

The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

For $2\leq p\leq \infty$, we establish dimension-free estimates for discrete dyadic Hardy-Littlewood maximal operators over Euclidean balls on semi-commutative $L_{p}$ space. In particular, when the radius is sufficiently large, these…

We establish sharp $L^p$ integral mean estimates for $(\alpha,\beta)$-harmonic functions on the unit disk. Explicit bounds for the functions and their partial derivatives are obtained in terms of boundary data, by means of the associated…

Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…

We establish a modified pointwise convex body domination for vector-valued Haar shifts in the nonhomogeneous setting, strengthening and extending the scalar case developed in arXiv:2309.13943. Moreover, we identify a subclass of shifts,…

The primary goal of this paper is to introduce bilinear analogues of uncentered spherical averages, Nikodym averages associated with spheres and the associated bilinear maximal functions. We obtain $L^p$-estimates for uncentered bilinear…

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…

A discussion of methods of nonisotropic fine quantitative complex analysis on lineally convex domains of finite type is given. The needed support functions with best possible estimates are considered together with the estimation of their…

In this note we extend N. Th. Varopoulos result on zero sets of H p functions of strictly pseudo-convex domains in C n to lineally convex domains of finite type.

We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…

This is a semi-expository article concerning Langlands functoriality and Deligne's conjecture on the special values of $L$-functions. The emphasis is on symmetric power $L$-functions associated to a holomorphic cusp form, while appealing to…

We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…

We study the holomorphic extendability of smooth CR maps between real analytic strictly pseudoconvex hypersurfaces in complex affine spaces of different dimensions.