A remark on differentiable functions with partial derivatives in Lp

Calogero Vetro; Cristina Di Bari; Cristina Di Bari; Calogero Vetro

A remark on differentiable functions with partial derivatives in Lp

Calogero Vetro, Cristina Di Bari, Cristina Di Bari, Calogero Vetro

Matematica e Informatica

Risultato della ricerca: Article › peer review

3 Citazioni (Scopus)

Abstract

We consider a definition of p, δ-variation for real functions of several variables which givesinformation on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

Lingua originale	English
pagine (da-a)	227-234
Numero di pagine	8
Rivista	Journal of Mathematical Analysis and Applications
Volume	299
Stato di pubblicazione	Published - 2004

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "We consider a definition of p, δ-variation for real functions of several variables which givesinformation on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Mal{\'y} and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.",

author = "Calogero Vetro and {Di Bari}, Cristina and {Di Bari}, Cristina and Calogero Vetro",

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AU - Di Bari, Cristina

AU - Vetro, Calogero

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AB - We consider a definition of p, δ-variation for real functions of several variables which givesinformation on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

UR - http://hdl.handle.net/10447/16702

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SP - 227

EP - 234

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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