On the Bourgain, Brezis, and Mironescu Theorem Concerning Limiting Embeddings of Fractional Sobolev Spaces

By Vladimir G. Maz'ya, T. Shaposhnikova. 2003

408 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f214bbfd3fc946eecc438a0093a452d55a65e9c0

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Fractional order Orlicz-Sobolev spaces (2017, background): “Mironescu in a series of papers [3, 4] (see also Maz’ya-Shaposhnikova [21] for the case s ↓ 0).”
Nonlocal problems with critical Hardy nonlinearity (2017, background): “The latter is well known in the cases α = 0 and α = ps, see [9] or [18].”
Fractional Caffarelli–Kohn–Nirenberg inequalities (2017, neutral): “1) using the results in [2], [3] and [7] (see Remark 2.”
Anisotropic fractional Sobolev norms (2013, background): “position 1([2]). Ifg ∈ W1,p(R) hascompactsupport,then lim s→1− (1− s) Z ∞ −∞ Z ∞ −∞ |g(x )− y p |x− y|1+ps dxdy = 2 p kgkp W1,p(R). We require the following one-dimensional case of (4). Proposition 2([28]). Ifg ∈ Ws,p(R) foralls ∈ (0,1),then lim s→0+ s Z ∞ −∞ Z ∞ −∞ |g(x)−g(y)|p |x− y|1+ps dxdy = 4 ”
Elliptic problems involving the fractional Laplacian in RN (2013, background): “1) where C2 2∗ = c(N) s(1−s) (N−2s) by Theorem 1 of [25], see also Theorem 1 of [7].”
Characterization of Sobolev and BV Spaces (2011, neutral): “[63] V. Maz’ya, T. Shaposhnikova, On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces.”
Non-linear ground state representations and sharp Hardy inequalities (2008, background): “(More precisely, these authors studied the corresponding problem for functions on a cube with zero average, but this problem is equivalent to the problem on the whole space, see [BBM2, Rem. 1] or [ MS1 , Cor.”
Pitt's inequality and the fractional Laplacian: Sharp error estimates (2007, background): “A brief sketch of this argument was given in [9].”
Fractional Orlicz-Sobolev embeddings (2020, background): “A touch of recent contributions in this connection is furnished by [7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 41, 44, 45, 51, 52, 53, 58, 59, 61, 62, 63, 64, 65, 68, 70, 71, 77, 76, 78, 83, 86].”