We introduce an approach to modular interpolation in this paper. By using this interpolation, we establish the modular inequalities for the Fourier transform, the Laplace transform, the Hankel transform and the oscillatory integral operators. Moreover, we also obtain the modular Fourier restriction theorem.
Cite this article
Kwok-Pun Ho, Modular interpolation and modular estimates of the Fourier transform and related operators. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 2, pp. 349–368DOI 10.4171/RLM/767