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279
Sobolev Embedding
, 2012
"... Purpose: Development of models to rigorgously describe manybody interactions and behavior of dynamical phenomena has suggested novel multilinear embedding estimates and forms that characterize fractional smoothness. This framework increases understanding for genuinely ndimensional aspects of Fouri ..."
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Purpose: Development of models to rigorgously describe manybody interactions and behavior of dynamical phenomena has suggested novel multilinear embedding estimates and forms that characterize fractional smoothness. This framework increases understanding for genuinely ndimensional aspects
ON HARDYSOBOLEV EMBEDDING
, 907
"... Abstract. Linear interpolation inequalities that combine Hardy’s inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to CaffarelliKohnNirenberg inequalities with sharp constants. A onedimensional convolut ..."
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Abstract. Linear interpolation inequalities that combine Hardy’s inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to CaffarelliKohnNirenberg inequalities with sharp constants. A onedimensional
An Elementary Proof Of Sharp Sobolev Embeddings
, 2000
"... We present an elementary unified and selfcontained proof of sharp Sobolev embedding theorems. We introduce a new function space and use it to improve the limiting Sobolev embedding theorem due to Brezis and Wainger. ..."
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Cited by 17 (1 self)
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We present an elementary unified and selfcontained proof of sharp Sobolev embedding theorems. We introduce a new function space and use it to improve the limiting Sobolev embedding theorem due to Brezis and Wainger.
On Improved Sobolev Embedding Theorems
"... .  We present a direct proof of some recent improved Sobolev inequalities put forward by A. Cohen, R. DeVore, P. Petrushev and H. Xu [CDVPX] in their wavelet analysis of the space BV (R 2 ). The argument, relying on pseudoPoincar'e inequalities, allows us to consider several extensions ..."
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Cited by 19 (0 self)
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.  We present a direct proof of some recent improved Sobolev inequalities put forward by A. Cohen, R. DeVore, P. Petrushev and H. Xu [CDVPX] in their wavelet analysis of the space BV (R 2 ). The argument, relying on pseudoPoincar'e inequalities, allows us to consider several
OPTIMAL GAUSSIAN SOBOLEV EMBEDDINGS
, 2009
"... A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangementinvariant norms with respect to the Gauss measure in Rn, is equivalent to a onedimensional inequality, for a suitable Hardytype operator, involving the same norms with respect to the standar ..."
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Cited by 10 (2 self)
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A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangementinvariant norms with respect to the Gauss measure in Rn, is equivalent to a onedimensional inequality, for a suitable Hardytype operator, involving the same norms with respect
Randomized Approximation of Sobolev Embeddings
"... We study approximation of functions belonging to Sobolev spaces W r p (Q) by randomized algorithms based on function values. Here 1 ≤ p ≤ ∞, Q = [0, 1] d, and r, d ∈ N. The error is measured in Lq(Q), with 1 ≤ q < ∞, and we assume r/d> 1/p − 1/q, guaranteeing that W r p (Q) is embedded into ..."
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We study approximation of functions belonging to Sobolev spaces W r p (Q) by randomized algorithms based on function values. Here 1 ≤ p ≤ ∞, Q = [0, 1] d, and r, d ∈ N. The error is measured in Lq(Q), with 1 ≤ q < ∞, and we assume r/d> 1/p − 1/q, guaranteeing that W r p (Q) is embedded
Optimal Sobolev embeddings on R^n
"... The aim of this paper is to study Sobolevtype embeddings and their optimality. We work in the frame of rearrangementinvariant norms and unbounded domains. We establish the equivalence of a Sobolev embedding to the boundedness of a certain Hardy operator on some cone of positive functions. This Ha ..."
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The aim of this paper is to study Sobolevtype embeddings and their optimality. We work in the frame of rearrangementinvariant norms and unbounded domains. We establish the equivalence of a Sobolev embedding to the boundedness of a certain Hardy operator on some cone of positive functions
Randomized Approximation of Sobolev Embeddings II
"... We study the approximation of Sobolev embeddings by linear randomized algorithms based on function values. Both the source and the target space are Sobolev spaces of nonnegative smoothness order, defined on a bounded Lipschitz domain. The optimal order of convergence is determined. We also study th ..."
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We study the approximation of Sobolev embeddings by linear randomized algorithms based on function values. Both the source and the target space are Sobolev spaces of nonnegative smoothness order, defined on a bounded Lipschitz domain. The optimal order of convergence is determined. We also study
Results 1  10
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279