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

We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the…

Avikainen showed that, for any $p,q \in [1,\infty)$, and any function $f$ of bounded variation in $\mathbb{R}$, it holds that $\mathbb{E}[|f(X)-f(\widehat{X})|^{q}] \leq C(p,q) \mathbb{E}[|X-\widehat{X}|^{p}]^{\frac{1}{p+1}}$, where $X$ is…

Let M be a smooth locally embeddable CR manifold, having some CR dimension m and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth…

Geometric lower and upper estimates are obtained for invariant metrics on $\Bbb C$-convex domains containing no complex lines.

We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.

Let $\Omega\subset\mathbb{C}^n$ be a strictly pseudoconvex Runge domain with $C^2$-smooth defining function, $l\in\mathbb{N},$ $p\in(1,\infty).$ We prove that the holomorphic function $f$ has derivatives of order $l$ in $H^p(\Omega)$ if and…

We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.

This is a companion to our previous paper. Here, we derive local dimension-free estimates for volumes of sub- and super-level sets of analytic functions of several variables.

We establish the $L^p$ restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address $L^p$ eigenfunction restriction estimates for Laplace-Beltrami…

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p in C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show…

Learning how to figure out sharp $L^p$-estimates of nonlinear differential expressions, to prove and use them, is a fundamental part of the development of PDEs and Geometric Function Theory (GFT). Our survey presents, among what is known to…

This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…

We consider the class $\Sigma(p)$ of univalent meromorphic functions $f$ on $\ID$ having simple pole at $z=p\in[0,1)$ with residue 1. Let $\Sigma_k(p)$ be the class of functions in $\Sigma(p)$ which have $k$-quasiconformal extension to the…

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the…

Let $X$ be a supermartingale starting from $0$ which has only nonnegative jumps. For each $0<p<1$ we determine the best constants $c_p$, $C_p$ and $\mathfrak{c}_p$ such that $$ \,\,\,\,\sup_{t\geq 0}\left|\left|X_t\right|\right|_p\leq…

In this work we prove a new $L^p$ holomorphic extension result for functions defined on product Lipschitz surfaces with small Lipschitz constants in two complex variables. We define biparameter and partial Cauchy integral operators that…

A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the…

In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale…

We consider nonconvex real valued functions whose truncations are either quasiconvex or even convex starting with a certain level. Among them, the $C^2$-smooth functions whose level sets are all completely contained in the positive definite…

We apply integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$ estimates for a given $(0,q)$-form, $f$, in terms of $C^k$ norms of $\mdbar f$,…