Some results of pseudo-differential operators related to the spherical mean operator

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-09-17 DOI:10.1007/s11868-024-00643-w

Khaled Hleili, Manel Hleili

引用次数: 0

Abstract

In this paper, we prove a potentially useful \(L^p(d\nu )\)-boundedness result for the pseudo-differential operators associated with the spherical mean operator. Also, boundedness result for symmetrically global pseudo-differential operator on \(L^p(d\nu )\)-type Sobolev space \(\mathcal {H}^{u,v,p}\) of order (u, v) are discussed. An application in solving a generalized heat equation is given.

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与球面均值算子有关的伪微分算子的一些结果

在本文中，我们证明了与（L^p(d\nu )）球均值算子相关的伪微分算子的一个潜在有用的（L^p(d\nu )）有界性结果。此外，我们还讨论了对称全局伪微分算子在阶（u, v）的 \(L^p(d\nu )\) 型 Sobolev 空间 \(\mathcal {H}^{u,v,p}\) 上的有界性结果。给出了在求解广义热方程中的应用。

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

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

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.