On the least values of Lp-norms for the Kontorovich–Lebedev transform and its convolution
In: Journal of Approximation Theory, Jg. 131 (2004-12-01), S. 231-242
Online
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Zugriff:
We establish analogs of the Hausdorff-Young and Riesz-Kolmogorov inequalities and the norm estimates for the Kontorovich-Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in Lp spaces, 1 ≤ p ≤ ∞. Boundedness properties of the Kontorovich-Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich-Lebedev operator Ki τ : Lp (R+;xdx) → Lp(R+;x sinh πx dx), 2 ≤ p ≤ ∞ Kiτ[f] = ∫0∞ Kiτ(x)f(x)dx, τ ∈ R+ is equal to π/21-1/p. It confirms, for instance, by the known Plancherel-type theorem for this transform when p = 2.
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On the least values of Lp-norms for the Kontorovich–Lebedev transform and its convolution
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Autor/in / Beteiligte Person: | Yakubovich, Semyon |
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Zeitschrift: | Journal of Approximation Theory, Jg. 131 (2004-12-01), S. 231-242 |
Veröffentlichung: | Elsevier BV, 2004 |
Medientyp: | unknown |
ISSN: | 0021-9045 (print) |
DOI: | 10.1016/j.jat.2004.10.007 |
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