Naslov
On the Hörmander-Mihlin theorem for mixed-norm Lebesgue spaces

Autori
Antonić, Nenad ; Ivec, Ivan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
PDEs, continuum mechanics and numerical analysis / Tambača, Josip i dr. - Zagreb, 2014, 15-15

Skup
PDEs, continuum mechanics and numerical analysis

Mjesto i datum
Dubrovnik, Hrvatska, 26.05.2014. - 30.05.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Hörmander-Mihlin theorem ; mixed-norm Lebesgue space

Sažetak
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 H¨ormander’s results (1960) on translation invariant operators on Lebesgue spaces extend to the mixed-norm case. We also revisit the H¨ormander- 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 Mitrovi´c and the first author) extension of H-measures, to these spaces.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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