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Fractional powers of operators, K-functionals, Ulyanov inequalities

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Trebels W., Westphal U.

Banach Center Publications

2010

tom 88

nr 1

273-283

Given an equibounded (𝓒₀)-semigroup of linear operators with generator A on a Banach space X, a functional calculus, due to L. Schwartz, is briefly sketched to explain fractional powers of A. Then the (modified) K-functional with respect to $(X,D((-A)^α))$, α > 0, is characterized via the associated resolvent R(λ;A). Under the assumption that the resolvent satisfies a Nikolskii type inequality, $||λR(λ;A)f||_Y ≤ cφ(1/λ)||f||_X$, for a suitable Banach space Y, an Ulyanov inequality is derived. This will be of interest if one has good control on the resolvent but not on the semigroup.

Ograniczanie wyników

1 Banach Center Publications

1 Trebels W.

1 Westphal U.

1 2010

Wyniki wyszukiwania

Fractional powers of operators, K-functionals, Ulyanov inequalities