Classical non-linear operators in Grand Lebesgue Spaces
M.R.Formica, E.Ostrovsky, L.Sirota
TL;DR
This paper investigates the boundedness of classical non-linear operators like Nemytskii, Urysohn, and Hammerstein within Grand Lebesgue Spaces, providing upper norm estimates and illustrative examples.
Contribution
It introduces new boundedness results for these operators in Grand Lebesgue Spaces, including precise upper norm estimates and examples demonstrating their sharpness.
Findings
Established boundedness of Nemytskii, Urysohn, Hammerstein operators in Grand Lebesgue Spaces
Derived explicit upper norm estimates for these operators
Provided examples confirming the sharpness of the estimates
Abstract
We study in this short report the boundedness of classical non-linear operators: Nemytskii, Urysohn, Hammerstein acting from one Grand Lebesgue Space to another one, and deduce some its upper norm estimates. We bring also some examples to illustrate the exactness of our estimates.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Approximation Theory and Sequence Spaces · Advanced Banach Space Theory