Fractional powers of operators, K-functionals, Ulyanov inequalities

Walter 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 -