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Muhammad Habiburrohman
Universitas Ivet
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Materials Science & Nanotechnology Physics

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Boundedness of Pseudo-Differential Operator for S0 Class Muhammad Habiburrohman; Dinni Rahma Oktaviani
Journal of Natural Sciences and Mathematics Research Vol 6, No 2 (2020): December
Publisher : Faculty of Science and Technology, Universitas Islam Negeri Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/jnsmr.2020.6.2.11219

Abstract

Pseudo-differential operator in a function space is obtained from the Fourier transform of this function space with a multiplier function. This paper will discuss and prove the boundedness of pseudo-differential operator in Lebesgue space with the multiplier function is in the class S0. The evolution of the pseudo-differential theory was then rapid. Based on development from this history, it has gave birth to the general definition of pseudo-differential operator that explain in this paper The general definition of pseudo-differential, of course has an applied or representation. One of them is the problem of partial differential equations in the Poisson equation  have the solution , and using Fourier transforms is obtained. In this case the form can be carried in the general form of a pseudo-differential operator. The  solution can be estimated for every if operator  is a bounded operator. In this paper, the operator defined with correspondes some symbol that describe this operator is more interest. The conclusion of this paper is the boundedness pseudo-differential operator , so we can estimated this number.©2020 JNSMR UIN Walisongo. All rights reserved.
Co-Authors Dinni Rahma Oktaviani