On the Hörmander-Mihlin theorem for mixed-norm Lebesgue spaces (CROSBI ID 219754)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Antonić, Nenad ; Ivec, Ivan
engleski
On the Hörmander-Mihlin theorem for mixed-norm Lebesgue spaces
For some questions in the theory of partial differential equations, it is useful to consider mixed-norm Lebesgue spaces introduced by Benedek and Panzone (1962). We show that Hörmander's results (1960) on translation invariant operators on Lebesgue spaces extend to the mixed-norm case. We also revisit the Hörmander- Mihlin multiplier theorem in this setting, which was first obtained by Lizorkin (1970), taking particular care to the form of constants in the estimates. This improvement allows us to prove the boundedness of classical pseudodifferential operators on mixed-norm Lebesgue spaces, as well as to generalise the H-distributions, a recently introduced (2011, by Mitrović and the first author) extension of H-measures, to these spaces.
Fourier multiplier ; Lebesgue space with mixed norm ; Pseudodifferential operator ; H-measure ; H-distribution
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Podaci o izdanju
433 (1)
2016.
176-199
objavljeno
0022-247X
1096-0813
10.1016/j.jmaa.2015.07.002