Interpolation of quasicontinuous functions

Joan Cerdà, Joaquim Martín, and Pilar Silvestre. "Interpolation of quasicontinuous functions." Banach Center Publications 95.1 (2011): 281-286. <http://eudml.org/doc/282488>.

@article{JoanCerdà2011,
abstract = {If C is a capacity on a measurable space, we prove that the restriction of the K-functional $K(t,f;L^p(C),L^∞(C))$ to quasicontinuous functions f ∈ QC is equivalent to $K(t,f;L^p(C) ∩ QC, L^∞(C) ∩ QC)$. We apply this result to identify the interpolation space $(L^\{p₀,q₀\}(C) ∩ QC,L^\{p₁,q₁\}(C) ∩ QC)_\{θ,q\}$.},
author = {Joan Cerdà, Joaquim Martín, Pilar Silvestre},
journal = {Banach Center Publications},
keywords = {capacity; Lorentz spaces; interpolation; quasicontinuous function},
language = {eng},
number = {1},
pages = {281-286},
title = {Interpolation of quasicontinuous functions},
url = {http://eudml.org/doc/282488},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Joan Cerdà
AU - Joaquim Martín
AU - Pilar Silvestre
TI - Interpolation of quasicontinuous functions
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 281
EP - 286
AB - If C is a capacity on a measurable space, we prove that the restriction of the K-functional $K(t,f;L^p(C),L^∞(C))$ to quasicontinuous functions f ∈ QC is equivalent to $K(t,f;L^p(C) ∩ QC, L^∞(C) ∩ QC)$. We apply this result to identify the interpolation space $(L^{p₀,q₀}(C) ∩ QC,L^{p₁,q₁}(C) ∩ QC)_{θ,q}$.
LA - eng
KW - capacity; Lorentz spaces; interpolation; quasicontinuous function
UR - http://eudml.org/doc/282488
ER -