Title: Characterization of Lipschitz functions in terms of variable exponent Lebesgue spaces,
Abstract: Our aim is to characterize the Lipschitz functions by variable exponent
Lebesgue spaces. We give some characterizations of the boundedness of the
maximal or nonlinear commutators of the Hardy-Littlewood maximal function and
sharp maximal function in variable exponent Lebesgue spaces when the symbols
$b$ belong to the Lipschitz spaces, by which some new characterizations of
Lipschitz spaces and nonnegative Lipschitz functions are obtained. Some
equivalent relations between the Lipschitz norm and the variable exponent
Lebesgue norm are also given.