Boundedness of Pseudo-Differential Operator for S0 Class
DOI:
https://doi.org/10.21580/jnsmr.2020.6.2.11219Keywords:
Pseudo-differential operator, the class S0, Fourier invers function, Lebesgue space.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.
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