Nontrivial examples of j n p and v j n p functions

HIGHLIGHTS

SUMMARY

A function f is in J N p (Q 0 ) if f ∈ L 1 (Q 0 ) and there is a constant K and amp;lt; ∞ such that p ∞ |Q i | | f - f Qi | ≤ K p i=1 Qi ∞ in Q. This follows from Hölder`s inequality: p ˆ ∞ ∞ ∞ |Q i | | f - f Qi | ≤ |Q i | | f - f Qi | p ≤ 2p | f |p (2.3) i=1 Qi i=1 Qi i=1 Qi ∞ of Q into disjoint cubes. The authors can estimate |K | ≤ |{x ∈ Q ∩ Q 0: x1 ∈ ∂ I }| ≤ |{x ∈ Q ∩ Q 0: x . . .

 



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