用于拉盖尔函数展开的同质贝索夫类型空间的分子分解及其应用

IF 0.9 3区 数学 Q2 MATHEMATICS
He Wang, Nan Zhao, Haihui Wang, Yu Liu
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引用次数: 0

摘要

在本文中,我们考虑了欧几里得空间 \(\mathbb R_{+}\) 上的拉盖尔算子(L=-\frac{d^2}{dx^2}-\frac{alpha }{x}\frac{d}{dx}+x^2\ )。本文的主要目的是发展与拉盖尔算子相关的同质贝索夫类型空间理论。为了实现我们的预期目标,我们引入了 \(\mathbb R_{+}\) 上的施瓦茨类型空间,然后构造了调和类型分布。利用拉盖尔算子的合适分布,我们建立了次谐函数的卡尔德龙重现公式和哈纳克类型不等式。有了这些工具,我们定义了贝索夫类型空间(\dot{B}_{p,q}^{s,L,m}/),并得到了\(\dot{B}_{p,q}^{s,L,m}/)的分子分解。作为应用,还研究了 Besov 型空间 \(\dot{B}_{p,q}^{s,L,m}\) 的嵌入定理和平方函数特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications

In this paper we consider the Laguerre operator \(L=-\frac{d^2}{dx^2}-\frac{\alpha }{x}\frac{d}{dx}+x^2\) on the Euclidean space \(\mathbb R_{+}\). The main aim of this article is to develop a theory of homogeneous Besov type spaces associated to the Laguerre operator. To achieve our expected goals, Schwartz type spaces on \(\mathbb R_{+}\) are introduced and then tempered type distributions are constructed. Using a suitable distribution of the Laguerre operator, the Calderón reproducing formula and the Harnack type inequality for subharmonic functions are established. With these tools in hand, we define the Besov type spaces \(\dot{B}_{p,q}^{s,L,m}\) and obtain the molecular decompositions of \(\dot{B}_{p,q}^{s,L,m}\). As applications, the embedding theorem and square functions characterization of Besov type spaces \(\dot{B}_{p,q}^{s,L,m}\) are also investigated.

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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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