Abstract
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.
Original language | English |
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Pages (from-to) | 69-91 |
Number of pages | 23 |
Journal | REVISTA MATEMATICA COMPLUTENSE |
Volume | 27 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2014 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Bounded (second)
- Bounded second (p, α) variation
- Fractional moduli of continuity
- Modulus of p p -continuity
- Partition
- Periodic function
- Steklov averages