Composition and commutator of pseudo-differential operators in the framework of zero-order Mehler-Fock transform domain

被引：0
|
作者：
Verma, Sandeep Kumar [1 ,2 ]
Prasad, Akhilesh [1 ]
机构：
[1] Indian Inst Technol ISM, Dept Math & Comp, Dhanbad 826004, Jharkhand, India
[2] SRM Univ AP, Dept Math, Amaravati 522503, Andhra Pradesh, India
来源：
JOURNAL OF ANALYSIS | 2023年 / 31卷 / 03期
关键词：
Pseudo-differential operator; Mehler-Fock transform; Legendre function; CONVOLUTION;
D O I：
10.1007/s41478-022-00531-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we discuss the boundedness and continuity of the pseudo-differential operator associated with the zero-order Mehler-Fock transform in Lebesgue space. We introduce the two versions of pseudo-differential operators P(u, A(u)) and Q(u, A(u)) involving the symbol class K and obtain their estimates in Lebesgue spaces. Further, we study the adjoint, composition, and commutator of the pseudo-differential operators in Hilbert space and obtain the boundedness of the commutator operator.
引用
收藏
页码：1753 / 1769
页数：17
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