We consider a definition of p, δ-variation for real functions of several variables which gives information 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.
DI BARI, C., VETRO, C. (2004). A remark on differentiable functions with partial derivatives in Lp. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 299(1), 227-234 [10.1016/j.jmaa.2004.06.044].
A remark on differentiable functions with partial derivatives in Lp
DI BARI, Cristina;VETRO, Calogero
2004-01-01
Abstract
We consider a definition of p, δ-variation for real functions of several variables which gives information 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.
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