Fourier transform is an important operation in the course"Functions of Complex Variables and Integral Transforms".The properties of the Fourier transform,in particular the convolution theorem,have a variety of applications in many fields.The main purpose of this paper is to study the boundedness of Hilbert transforms in the field of harmonic analysis in view of the Fourier transform and the convolution theorem.Further,it reflects that the Fourier transform plays an important role in the research of harmonic analysis theory.
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