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- W2398117584 abstract "We show that if R N , N 2, is a bounded Lipschitz domain and ( n) L 1 (R N ) is a sequence of nonnegative radial functions weakly converging to 0, then Z |f f | p C Z Z |f(x) f(y)| p |x y|p n (|x y|) dxdy for all f 2 L p ( ) and n n0, where f denotes the average of f on . The above estimate was suggested by some recent work of Bourgain, Brezis and Mironescu (2). As n ! 1 we recover Poincare's inequality. The case N = 1 requires an additional assumption on ( n). We also extend a compactness result of Bourgain, Brezis and Mironescu." @default.
- W2398117584 created "2016-06-24" @default.
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- W2398117584 date "2003-01-01" @default.
- W2398117584 modified "2023-09-26" @default.
- W2398117584 title "An estimate in the spirit of Poincare's" @default.
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