2 Let p [member of] [1, [infinity]) and let g : R [right arrow] C be a locally absolutely continuous function
with g and g' belonging to [L.
It is easy to see that for any locally absolutely continuous function f: [a, b] [right arrow] R, we have the identity
respectively, and to seek sharp upper bounds for these distances in terms of different measure that can be associated with f, where f is restricted to particular classes of functions including functions of bounded variation, Lipschitzian, convex and absolutely continuous functions.
2) is an absolutely continuous function, which satisfies that equation on (0, [infinity]) almost everywhere and condition (1.
4) is defined as a locally absolutely continuous function x(t), with [?
for x [member of] [a, b] where f : [a, b] [right arrow] R is an absolutely continuous function on [a, b].
Let f and g : [a, b] [right arrow] R be absolutely continuous functions on [a, b].
The rate is best possible amongst absolutely continuous functions f on [-1, 1] whose derivative is bounded.
for all absolutely continuous functions f : R [right arrow] R for which f (0) = 0 and the right-hand side is finite.
loc] refers to the class of locally absolutely continuous functions