On Peano derivatives in $L^{p}(E_{n})$

S. Lasher

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Displaying similar documents to “On Peano derivatives in $L^{p} (E_{n})$ ”

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Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. $L^{p}$ , 1 ≤ p ≤ ∞) sense at $x \in ℝ^{m}$ if there are numbers $f_{α} (x)$ , |α| ≤ n, such that $f (x + h) - \sum_{| α | \leq n} f_{α} (x) h^{α} / α!$ is $O (h^{u})$ in the approximate (resp. $L^{p}$ ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or $L^{p}$ sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and...

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Asymptotic nature of higher Mahler measure

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Displaying similar documents to “On Peano derivatives in L p ( E n ) ”

Displaying similar documents to “On Peano derivatives in $L^{p} (E_{n})$ ”