The Kontorovich-Lebedev Transform and Sobolev Type Space

被引：7

作者：

Prasad, Akhilesh ^{[1
]}

Mandal, U. K. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Appl Math, Indian Sch Mines, Dhanbad 826004, Bihar, India

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2018年 / 12卷 / 03期

关键词：

Kontorovich-Lebedev transform; Convolution; Pseudo-differential operator; Banach space;

D O I：

10.1007/s11785-017-0734-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper boundedness of convolution operator in is given and continuity of pseudo-differential operator associated with the Kontorovich-Lebedev transform (KL-transform) from into itself is discussed. The Kontorovich-Lebedev potential (KL-potential) is defined on and then it is extended to the space of distributions also some of its properties are studied. A Sobolev type space associated with the KL-transform is discussed and proved as a Banach space. Moreover, it is shown that the KL-potential is an isometry of . An -boundedness for the KL-potential is obtained and at the end applications of the KL-potential in pseudo-differential equation are discussed.

引用

页码：669 / 681

页数：13

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