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We will investigate properties of functions in the Wiener class BVp[a,b] with 0<p<1. We prove that any function in BVp[a,b] (0<p<1) can be expressed as the difference of two increasing functions in BVp[a,b]. We also obtain the explicit form of functions in BVp[a,b] and show that their derivatives are equal to zero a.e. on [a,b]

journal of function spaces

Properties of Functions in the Wiener Class<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>B</mml:mi><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">[</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:math>for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mn>0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>p</mml:mi><mml:mo>&lt;</…

Properties of Functions in the Wiener ClassBVp[a,b]for0<p<