General monotonicity, interpolation of operators, and applications

General monotonicity, interpolation of operators, and applications

We continue the work of S. Tikhonov, E. Liflyand, B. Booton, and others, proving the equivalence of L(p,q)-norms of general monotone functions and of their Fourier transforms. The main tool in this work is the interpolation properties of cones of general monotone functions in L(p,q)-norms.

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Veröffentlicht in:arXiv.org 2014-10
Hauptverfasser: Grigoriev, S M, Sagher, Y, Savage, T R
Format: Artikel
Sprache:eng
Schlagworte:
Cones
Fourier transforms
Interpolation
Monotone functions
Norms
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Zusammenfassung:We continue the work of S. Tikhonov, E. Liflyand, B. Booton, and others, proving the equivalence of L(p,q)-norms of general monotone functions and of their Fourier transforms. The main tool in this work is the interpolation properties of cones of general monotone functions in L(p,q)-norms.
ISSN:2331-8422