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Title: Lp-Lq Fourier multipliers on locally compact groups
Author: Akylzhanov, Rauan
ISNI:       0000 0004 7427 7520
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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We study the Lp − Lq boundedness of both spectral and Fourier multi- pliers on general locally compact separable unimodular groups G. As a consequence of the established Fourier multiplier theorem we also derive a spectral multiplier theorem on general locally compact separable uni- modular groups. We then apply it to obtain embedding theorems as well as time-asymptotics for the Lp − Lq norms of the heat kernels for general positive unbounded invariant operators on G. We illustrate the obtained results for sub-Laplacians on compact Lie groups and on the Heisenberg group, as well as for higher order operators. With minor modificaitons, our proofs of Paley-type inequalities and Lp − Lq bounds of Fourier multipliers can be adapted to the setting of compact homogeneous manifolds.
Supervisor: Ruzhansky, Michael Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral