The generalized functionals of Merentes type generate a scale of spaces connecting the class of functions of bounded second p p -variation with the Sobolev space of functions with p-integrable second derivative. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of order 2 - 1 / p. These results extend the results in Lind (Math Inequal Appl 16:2139, 2013) for functions of bounded variation but are not consequence of the last.
- Bounded (second)
- Bounded second (p, α) variation
- Fractional moduli of continuity
- Modulus of p p -continuity
- Periodic function
- Steklov averages