Harmonic Bergman Projectors on Homogeneous Trees

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-10-13 DOI:10.1007/s11118-023-10106-4

Filippo De Mari, Matteo Monti, Maria Vallarino

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引用次数: 2

Abstract

Abstract In this paper we investigate some properties of the harmonic Bergman spaces $$\mathcal A^p(\sigma )$$ A p ( σ ) on a q -homogeneous tree, where $$q\ge 2$$ q ≥ 2 , $$1\le p<\infty $$ 1 ≤ p < ∞ , and $$\sigma $$ σ is a finite measure on the tree with radial decreasing density, hence nondoubling. These spaces were introduced by J. Cohen, F. Colonna, M. Picardello and D. Singman. When $$p=2$$ p = 2 they are reproducing kernel Hilbert spaces and we compute explicitely their reproducing kernel. We then study the boundedness properties of the Bergman projector on $$L^p(\sigma )$$ L p ( σ ) for $$1 1 < p < ∞ and their weak type (1,1) boundedness for radially exponentially decreasing measures on the tree. The weak type (1,1) boundedness is a consequence of the fact that the Bergman kernel satisfies an appropriate integral Hörmander’s condition.

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齐次树上的谐波Bergman投影

摘要本文研究了q -齐次树上的调和Bergman空间$$\mathcal A^p(\sigma )$$ A p (σ)的一些性质，其中$$q\ge 2$$ q≥2,$$1\le p<\infty $$ 1≤p ＆lt;∞，且$$\sigma $$ σ是密度呈径向递减的树的有限测度，因此不加倍。这些空间由J. Cohen、F. Colonna、M. Picardello和D. Singman引入。当$$p=2$$ p = 2时，它们正在再现核希尔伯特空间，我们显式地计算它们的再现核。然后研究了$$1<p<\infty $$ 1 ＆lt下$$L^p(\sigma )$$ L p (σ)上Bergman投影的有界性;P ＆lt;∞和它们的弱型(1,1)有界性。弱型(1,1)有界性是Bergman核满足适当的积分Hörmander条件的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.