Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

• Autorzy: Thomas Kühn , Mieczysław Mastyło
• Języki publikacji: EN

Abstrakty

EN

We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also able to show the optimality of our eigenvalue estimates in the Lorentz spaces $L_{2,q}$ with 1 ≤ q < 2 and in Zygmund spaces $L_{p}(log L)_a$ with 2 ≤ p < ∞ and a > 0.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 47G10: Integral operators
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s -numbers, Kolmogorov numbers, entropy numbers, etc. of operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 207
• Numer: 3
• Strony: 275-296

Daty

wydano

2011

Twórcy

autor

Thomas Kühn

• Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Johannisgasse 26, D-04103 Leipzig, Germany

autor

Mieczysław Mastyło

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University
• Institute of Mathematics, Polish Academy of Sciences (Poznań branch), Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm207-3-4