Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

A dramatização da crise dos valores sociais e humanos em Tess of the d'Urbervilles, de Thomas Hardy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Thomas Hardy: Tess von d'Urbervilles [Rezension]

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Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.