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L^p-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

Steve Hofmann
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      The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local $T(b)$ theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for $L^p$ and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
      Format: Paperback / softback CONTRIBUTORS: Steve Hofmann EAN: 9781470422608 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-01-01 CITY: GENRE: MATHEMATICS / General WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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      Steve Hofmann, University of Missouri, Columbia.Dorina Mitrea, University of Missouri, Columbia.Marius Mitrea, University of Missouri, Columbia.Andrew J. Morris, University of Missouri, Columbia.
      The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local $T(b)$ theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for $L^p$ and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
      Format: Paperback / softback CONTRIBUTORS: Steve Hofmann EAN: 9781470422608 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-01-01 CITY: GENRE: MATHEMATICS / General WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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      Steve Hofmann, University of Missouri, Columbia.Dorina Mitrea, University of Missouri, Columbia.Marius Mitrea, University of Missouri, Columbia.Andrew J. Morris, University of Missouri, Columbia.

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