On the hyperbolic group and subordinated integrals as operators on sequence Banach spaces

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-09-15 DOI:10.1007/s10476-024-00047-4

L. Abadias, J. E. Galé, P. J. Miana, J. Oliva-Maza

引用次数: 0

Abstract

We show that the composition hyperbolic group in the unit disc, once transferred to act on sequence spaces, is bounded on \(\ell^p\) if and only if \({p=2}\). We introduce some integral operators subordinated to that group which are natural generalizations of classical operators on sequences. For the description of such operators, we use some combinatorial identities which look interesting in their own.

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论序列巴拿赫空间上作为算子的双曲群和次积分

我们证明，单位圆盘中的组成双曲群一旦转移到作用于序列空间，当且仅当\({p=2}\)时，它在\(\ell^p\)上是有界的。我们将介绍一些从属于该组的积分算子，它们是序列上经典算子的自然概括。为了描述这些算子，我们使用了一些本身看起来就很有趣的组合等式。

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

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.