A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I

It is shown that the space of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause, defined on a rectangle Iab⊂Rn, is a Banach algebra under the pointwise operations and Hildebrandt-Leonov's norm. This result generalizes the classical case of functions of bounded Jordan variation on an interval Iab=[a,b] for n=1 and a previous result of the author in [Monatsh. Math. 137(2) (2002) 99-114] for n=2.