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Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications

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Abstract

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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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    He Wang, Nan Zhao & Yu Liu

  2. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Haihui Wang

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  1. He Wang
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He Wang and Nan Zhao wrote the main manuscript text, Haihui Wang and Yu Liu modified the text. All authors reviewed the manuscript.

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Correspondence to Yu Liu.

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Y. Liu was supported by the Beijing Natural Science Foundation of China (No. 1232023) and the National Natural Science Foundation of China (No. 12271042), and H.H. Wang was supported by the National Science and Technology Major Project of China (No. J2019-I-0019-0018, No. J2019-I-0001-0001).

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Wang, H., Zhao, N., Wang, H. et al. Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications. J. Pseudo-Differ. Oper. Appl. 15, 14 (2024). https://doi.org/10.1007/s11868-024-00587-1

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