Boundedness of Mikhlin Operator in Morrey Space

Abstract

A multiplier operator is an operator which maps a function to the product of that function with a certain function. A Fourier multiplier operator is a multiplier operator which use Fourier transformation of a function. S. G. Mikhlin proved the boundedness of the operator in classical Lebesgue space if the multiplier function (generator of the Fourier multiplier operator) is a bounded function. In this paper, we prove that Fourier multiplier operator is also bounded on classical Morrey space which is greater than the Lebesgue space.