Abstract
In this chapter we overview the technique of interpolation of operators, which is widely used in harmonic analysis in connection with Lebesgue spaces. The underlying idea is to obtain boundedness of an operator based on the available information in the endpoints. In the first section we will deal with the Riesz-Thorin interpolation theorem, also known as the complex method, and give some applications, viz. Hausdorff-Young inequality and Young’s inequality for convolution. In the second section we prove the Marcinkiewicz interpolation theorem in Lebesgue spaces and also mention the theorem in its natural environment, namely in the framework of Lorentz spaces. We end the chapter with the Young’s convolution inequality in Lorentz spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
