Harmonic Bergman Projectors on Homogeneous Trees

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.