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Related papers: An estimate for narrow operators on $L^p([0, 1])$

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We prove sharp $L^p-L^q$ estimates for averaging operators along general polynomial curves in two and three dimensions. These operators are translation-invariant, given by convolution with the so-called affine arclength measure of the curve…

Classical Analysis and ODEs · Mathematics 2008-07-07 Spyridon Dendrinos , Norberto Laghi , James Wright

We present a complete characterization of the metric compactification of $L_{p}$ spaces for $1\leq p < \infty$. Each element of the metric compactification of $L_{p}$ is represented by a random measure on a certain Polish space. By way of…

Functional Analysis · Mathematics 2022-06-01 Armando W. Gutiérrez

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

Classical Analysis and ODEs · Mathematics 2016-02-08 Robert S. Rahm , Brett D. Wick

We prove an algorithmic regularity lemma for $L_p$ regular matrices $(1 < p \leq \infty),$ a class of sparse $\{0,1\}$ matrices which obey a natural pseudorandomness condition. This extends a result of Coja-Oghlan, Cooper and Frieze who…

Combinatorics · Mathematics 2017-05-19 Thodoris Karageorgos , Silouanos Brazitikos

For $1<p<\infty$, we prove (i) a version of Voiculescu's absorption theorem for operators on $l^{p}$, (ii) that $\mathrm{Ext}_{\sim,s}(\mathcal{A},K(l^{p}))$ is a group for certain Banach algebra $\mathcal{A}$, and (iii) homotopy invariance…

Functional Analysis · Mathematics 2019-09-24 March T. Boedihardjo

We prove an $L^{p}$ estimate $$ \|e^{-itL} \varphi(L)f\|_{p}\lesssim (1+|t|)^s\|f\|_p, \qquad t\in \mathbb{R}, \qquad s=n\left|\frac{1}{2}-\frac{1}{p}\right| $$ for the Schr\"odinger group generated by a semibounded, selfadjoint operator…

Analysis of PDEs · Mathematics 2019-07-25 The Anh Bui , Piero D'Ancona , Fabio Nicola

Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the…

Complex Variables · Mathematics 2020-05-19 Yunus E. Zeytuncu

A result of Chernoff gives sufficient condition for an $L^2$-function on $\R^n$ to be quasi-analytic. This is a generalization of the classical Denjoy-Carleman theorem on $\R$ and of the subsequent work on $\R^n$ by Bochner and Taylor. In…

Functional Analysis · Mathematics 2022-04-29 Rudra P. Sarkar

We obtain (weighted) restricted type estimates for the Bergman projection operator on monomial polyhedra, a class of domains generalizing the Hartogs triangle. From these estimates, we recapture $L^p$ boundedness results of the Bergman…

Complex Variables · Mathematics 2025-03-03 Debraj Chakrabarti , Zhenghui Huo

We prove that order zero operators in the pseudodifferential calculus associated to a filtration defined by Androulidakis, Mohsen and Yuncken are bounded on $L_p$ spaces for $1<p<\infty.$

Functional Analysis · Mathematics 2026-02-19 Edward McDonald

We propose practical algorithms for entrywise $\ell_p$-norm low-rank approximation, for $p = 1$ or $p = \infty$. The proposed framework, which is non-convex and gradient-based, is easy to implement and typically attains better…

Machine Learning · Computer Science 2018-05-25 Anastasios Kyrillidis

Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…

Classical Analysis and ODEs · Mathematics 2010-02-07 Michael Greenblatt

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…

Functional Analysis · Mathematics 2021-05-12 Raffael Hagger , Christian Seifert

We get the sharp bound for weak type $(1,1)$ inequality for $n$-dimensional Hardy operator. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are obtained. As applications, the corresponding norms of…

Functional Analysis · Mathematics 2021-11-09 Fayou Zhao , Zunwei Fu , Shanzhen Lu

We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.

Functional Analysis · Mathematics 2012-08-17 Miguel Lacruz

We prove sharp $L^p$ estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their $L^2$ norms on the boundary. We prove it by establishing $L^p$ bounds for the harmonic extension operators as well as the…

Analysis of PDEs · Mathematics 2023-01-03 Xiaoqi Huang , Yannick Sire , Xing Wang , Cheng Zhang

We characterize positivity preserving, translation invariant, linear operators in $L^p(\mathbb{R}^n)^m$, $p \in [1,\infty)$, $m,n \in \mathbb{N}$.

Functional Analysis · Mathematics 2017-12-15 Fritz Gesztesy , Michael M. H. Pang

In this article we prove L^p estimates for a general maximal operator, which extend both the classical Coifman-Meyer and Carleson-Hunt theorems in harmonic analysis

Classical Analysis and ODEs · Mathematics 2007-05-23 Xiaochun Li , Camil Muscalu

The purpose of this paper is to give an estimate of the $L^p$-norm of the Bergman projection on the Hartogs triangle.

Complex Variables · Mathematics 2017-03-16 Tomasz Beberok

We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vall\'{e}e Poussin operator will also be given.

Classical Analysis and ODEs · Mathematics 2019-04-08 Wlodzimierz Lenski , Bogdan Szal
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