Garello, Gianluca and Morando, Alessandro:
$L^p$-boundedness for pseudodifferential operators with non-smooth symbols and applications
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.2, p. 461-503, Unione Matematica Italiana (English)
pdf (464 Kb), djvu (561 Kb). | MR2149396 | Zbl 1178.35395
Sunto
Utilizzando una formulazione generalizzata della caratterizzazione per corone diadiche degli spazi di Sobolev, nel presente lavoro si dimostra la continuità $L^{p}$ per operatori pseudodifferenziali il cui simbolo a(x,ξ) non è infinitamente differenziabile rispetto alla variabile x, mentre le sue derivate rispetto alla variabile ξ decadono con ordine ρ, con $0 < \rho \leq 1$. Viene poi provata una proprietà di algebra per una classe di spazi di Sobolev pesati, che ben si applica allo studio della regolarità delle soluzioni di equazioni semi lineari multi-quasi-ellittiche.
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