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## Second commutation lemma for fractional H-measures

Erceg, Marko; Ivec, Ivan
Second commutation lemma for fractional H-measures // Journal of Pseudo-Differential Operators and Applications, 9 (2018), 3; 589-613 doi:10.1007/s11868-017-0207-y (međunarodna recenzija, članak, znanstveni)

Naslov
Second commutation lemma for fractional H-measures

Autori
Erceg, Marko ; Ivec, Ivan

Izvornik
Journal of Pseudo-Differential Operators and Applications (1662-999X) 9 (2018), 3; 589-613

Ključne riječi
H-measures ; fractional derivatives ; propagation principle

Sažetak
Classical H-measures introduced by Tartar (1990) and independently by Gérard (1991) are essentially suited for hyperbolic equations while parabolic equations fit in the framework of the parabolic H-measures developed by Antonić and Lazar (2007--2013). More recently the study of differential relations with fractional derivatives prompted the extension of the theory to arbitrary ratios, thus the fractional H- measures were introduced and applied to fractional conservation laws by Mitrović and Ivec (2011). In this paper we explore the transport property of fractional H-measures by studying fractional derivatives of commutators of multiplication and Fourier multiplier operators. In particular, we prove the Second commutation lemma suitable for fractional H- measures, comprehending the known hyperbolic and parabolic cases, while allowing for derivation of the corresponding propagation principle for fractional H-measures. At the end, on a model example we present this derivation of the transport equation for the fractional H-measure.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
HRZZ-IP-2013-11-9780 - Metode slabih convergencija i primjene (Nenad Antonić, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb,
Metalurški fakultet, Sisak

Autor s matičnim brojem:
Ivan Ivec, (339756)
Marko Erceg, (335546)

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI