Functions of bounded second p p -variation

Sorina Barza; Pilar Silvestre Albero

doi:10.1007/s13163-013-0136-0

Functions of bounded second p p -variation

Sorina Barza, Pilar Silvestre Albero

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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
Pages (from-to)	69-91
Number of pages	23
Journal	REVISTA MATEMATICA COMPLUTENSE
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s13163-013-0136-0
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

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KW - Bounded second (p, α) variation

KW - Fractional moduli of continuity

KW - Modulus of p p -continuity

KW - Partition

KW - Periodic function

KW - Steklov averages

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