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On the Carleson duality

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Title: On the Carleson duality
Authors: Hytönen, Tuomas, Rosén, Andreas, 1974
Source: Arkiv for Matematik. 51(2):293-313
Subject Terms: non-tangential maximal function, Carleson’s inequality, dyadic model.
Description: As a tool for solving the Neumann problem for divergence form equations, Kenig and Pipher introduced the space X of functions on the half space, such that the non-tangential maximal function of their L_2-Whitney averages belongs to L_2 on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of X, and characterize the pointwise multipliers from X to L_2 on the half space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to L_p generalizations of the space X. Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.
Access URL: https://research.chalmers.se/publication/207376
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  – Url: https://dx.doi.org/doi:10.1007/s11512-012-0167-7
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  Data: On the Carleson duality
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  Data: <searchLink fieldCode="AR" term="%22Hytönen%2C+Tuomas%22">Hytönen, Tuomas</searchLink><br /><searchLink fieldCode="AR" term="%22Rosén%2C+Andreas%22">Rosén, Andreas</searchLink>, 1974
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  Data: <i>Arkiv for Matematik</i>. 51(2):293-313
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  Data: <searchLink fieldCode="DE" term="%22non-tangential+maximal+function%22">non-tangential maximal function</searchLink><br /><searchLink fieldCode="DE" term="%22Carleson%27s+inequality%22">Carleson’s inequality</searchLink><br /><searchLink fieldCode="DE" term="%22dyadic+model%2E%22">dyadic model.</searchLink>
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  Data: As a tool for solving the Neumann problem for divergence form equations, Kenig and Pipher introduced the space X of functions on the half space, such that the non-tangential maximal function of their L_2-Whitney averages belongs to L_2 on the boundary. In this paper, answering questions which arose from recent studies of boundary value problems by Auscher and the second author, we find the pre-dual of X, and characterize the pointwise multipliers from X to L_2 on the half space as the well-known Carleson-type space of functions introduced by Dahlberg. We also extend these results to L_p generalizations of the space X. Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.
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        Value: 10.1007/s11512-012-0167-7
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      – Text: English
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        PageCount: 21
        StartPage: 293
    Subjects:
      – SubjectFull: non-tangential maximal function
        Type: general
      – SubjectFull: Carleson’s inequality
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            NameFull: Rosén, Andreas
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            – D: 01
              M: 01
              Type: published
              Y: 2013
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