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Inequalities for poisson integrals with slowly growing dimensional constants
Grafakos, Loukas (University of Missouri. Department of Mathematics)
Laeng, Enrico (Politecnico di Milano. Dipartimento di Matematica)
Morpurgo, Carlo (University of Missouri. Department of Mathematics)

Data: 2007
Resum: Let Pt be the Poisson kernel. We study the following Lp inequality for the Poisson integral P f(x, t) = (Pt ∗ f)(x) with respect to a Carleson measure µ: L p(R n+1 + ,dµ) ≤ cp,nκ(µ) 1 p L p(Rn,dx) , where 1 < p < ∞ and κ(µ) is the Carleson norm of µ. It was shown by Verbitsky [V] that for p > 2 the constant cp,n can be taken to be independent of the dimension n. We show that c2,n = O((log n) 1 2 ) and that cp,n = O(n 1 p − 1 2 ) for 1 < p < 2 as n → ∞. We observe that standard proofs of this inequality rely on doubling properties of cubes and lead to a value of cp,n that grows exponentially with n. P f.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Carleson measures ; Harmonic functions ; Dimension free estimates
Publicat a: Publicacions matemàtiques, Vol. 51 Núm. 1 (2007) , p. 59-75, ISSN 2014-4350

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DOI: 10.5565/PUBLMAT_51107_04

17 p, 201.7 KB

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