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

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 View the MathML sourceIab⊂Rn, is a Banach algebra under the pointwise operations and Hildebrandt–Leonovʹs norm. This result generalizes the classical case of functions of bounded Jordan variation on an interval View the MathML sourceIab=[a,b] for n=1n=1 and a previous result of the author in [Monatsh. Math. 137(2) (2002) 99–114] for n=2n=2.