A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1

• Autorzy: Stefan Geiss , Paul F. X. Müller , Veronika Pillwein
• Języki publikacji: EN

Abstrakty

EN

For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$, 0 < s < 2, to be the linear extension of the map
$(h_{I})/(|I|^{1/s}) ↦ (h_{τ(I)})(|τ(I)|^{1/s})$,
where $h_{I}$ denotes the $L^{∞}$-normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s₀}$ is bounded on $H^{s₀}$, then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 46B70: Interpolation between normed linear spaces
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 2
• Strony: 196-205

Daty

wydano

2005

Twórcy

autor

Stefan Geiss

• Department of Mathematics and Statistics, P.O. Box 35 (MaD), FIN-40014 University of Jyväskylä, Finland

autor

Paul F. X. Müller

• Department of Analysis, J. Kepler University, A-4040 Linz, Austria

autor

Veronika Pillwein

• Department of Analysis, J. Kepler University, A-4040 Linz, Austria

Identyfikatory

DOI

10.4064/sm171-2-5