Lions-Peetre reiteration formulas for triples and their applications

• Autorzy: Irina Asekritova , Natan Krugljak , Lech Maligranda , Lyudmila Nikolova , Lars-Erik Persson
• Języki publikacji: EN

Abstrakty

EN

We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted $L_{p}$-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein-Weiss interpolation theorem known for $L_{p}(μ)$-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.

Kategorie tematyczne

• 42C99: None of the above, but in this section
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B70: Interpolation between normed linear spaces
• 46M35: Abstract interpolation of topological vector spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 145
• Numer: 3
• Strony: 219-254

Daty

wydano

2001

Twórcy

autor

Irina Asekritova

• Department of Mathematics, Yaroslavl' State Pedagogical University, Respublikanskaya 108, 150 000 Yaroslavl', Russia

autor

Natan Krugljak

• Department of Mathematics, Yaroslavl' State University, Sovetskaya 14, 150 000 Yaroslavl', Russia

autor

Lech Maligranda

• Department of Mathematics, Luleå University of Technology, S-971 87 Luleå, Sweden

autor

Lyudmila Nikolova

• Department of Mathematics, Sofia University, blv. J. Bouchier 5, 1164 Sofia, Bulgaria

autor

Lars-Erik Persson

• Department of Mathematics, Luleå University of Technology, S-971 87 Luleå, Sweden

Identyfikatory

DOI

10.4064/sm145-3-4