منابع مشابه
On some pointwise inequalities
In a recent paper (Studia Math. 138 (2000) 285–291) we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that, in a sense, there are more flexible inequalities which not only imply the previously known results but also give something new. In particular, they hold for the multilinear Calderón–Zygmund operators. This result gives a new approa...
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We establish pointwise characterizations of functions in the HardySobolev spaces H within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H(R) if and only if u ∈ L(R) and it satisfies the Hajlasz type condition |u(x)− u(y)| ≤ |x − y|(h(x) + h(y)), x, y ∈ R \ E, where E is a set of measure zero and h ∈ L(R). We also investigate HardySobolev spaces on subdo...
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Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...
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We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. 0. Introduction Suppose Ω ⊂ R is a bounded domain and let d(x) = dist(x, ∂Ω). We consider integral Hardy inequalities (0.1) ∀u ∈ ...
متن کاملImproved Hardy-sobolev Inequalities
Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04495-0