# Fractional powers of operators, K-functionals, Ulyanov inequalities

Walter Trebels; Ursula Westphal

Banach Center Publications (2010)

- Volume: 88, Issue: 1, page 273-283
- ISSN: 0137-6934

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topWalter Trebels, and Ursula Westphal. "Fractional powers of operators, K-functionals, Ulyanov inequalities." Banach Center Publications 88.1 (2010): 273-283. <http://eudml.org/doc/282573>.

@article{WalterTrebels2010,

abstract = {Given an equibounded (₀)-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.},

author = {Walter Trebels, Ursula Westphal},

journal = {Banach Center Publications},

keywords = { semigroup; -functional; Ulyanov inequality},

language = {eng},

number = {1},

pages = {273-283},

title = {Fractional powers of operators, K-functionals, Ulyanov inequalities},

url = {http://eudml.org/doc/282573},

volume = {88},

year = {2010},

}

TY - JOUR

AU - Walter Trebels

AU - Ursula Westphal

TI - Fractional powers of operators, K-functionals, Ulyanov inequalities

JO - Banach Center Publications

PY - 2010

VL - 88

IS - 1

SP - 273

EP - 283

AB - Given an equibounded (₀)-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.

LA - eng

KW - semigroup; -functional; Ulyanov inequality

UR - http://eudml.org/doc/282573

ER -