Erratum : Notes on interpolation of Hardy spaces
Quanhua Xu (1993)
Annales de l'institut Fourier
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An error in the paper named in the title ibid., 42-4 (1992)875-889 is corrected.
Quanhua Xu (1993)
Annales de l'institut Fourier
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An error in the paper named in the title ibid., 42-4 (1992)875-889 is corrected.
John B. Garnett (1978)
Annales de l'institut Fourier
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Let be a sequence in the upper half plane. If and if has solution in the class of Poisson integrals of functions for any sequence , then we show that is an interpolating sequence for . If , has solution in the class of Poisson integrals of BMO functions whenever , then is again an interpolating sequence for . A somewhat more general theorem is also proved and a counterexample for the case is described.
W. K. Hayman (1958)
Annales de l'institut Fourier
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Soit un domaine plan ; y a-t-il des suites telles que toute suite bornée puisse être interpolée en par une fonction régulière et bornée dans ? Dans l’affirmative est-il vrai que toute suite qui tend assez rapidement vers la frontière de possède cette propriété ? On répond affirmativement à ces deux questions dans le cas où est le cercle-unité.
V. Kolyada (1997)
Studia Mathematica
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We investigate the Fourier transforms of functions in the Sobolev spaces . It is proved that for any function the Fourier transform f̂ belongs to the Lorentz space , where . Furthermore, we derive from this result that for any mixed derivative the weighted norm can be estimated by the sum of -norms of all pure derivatives of the same order. This gives an answer to a question posed by A. Pełczyński and M. Wojciechowski.
Frank Mantlik (1991)
Annales de l'institut Fourier
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Let be a differential operator with constant coefficients depending analytically on a parameter . Assume that the family P(,D) is of constant strength. We investigate the equation where is a given analytic function of with values in some space of distributions and the solution is required to depend analytically on , too. As a special case we obtain a regular fundamental solution of P(,D) which depends analytically on . This result answers a question of L. Hörmander. ...
M. Grigorian (1999)
Studia Mathematica
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It is proved that if is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form , where for all q>2, with the following properties: 1. For any p ∈ [1,2) and there are numbers , k=1,2,…, = 1 or 0, such that 2. For every p ∈ [1,2) and there are a function with g(x) = f(x) on E and numbers , k=1,2,…, or 0,...
Jean-Loup Mauclaire (2000)
Journal de théorie des nombres de Bordeaux
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Let , be a Cantor scale, the compact projective limit group of the groups , identified to , and let be its normalized Haar measure. To an element , of we associate the sequence of integral valued random variables . The main result of this article is that, given a complex -multiplicative function of modulus , we have