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Lp-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets / Steve Hofmann...[et al.].

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 245, no 1159.Publication details: Providence : American Mathematical Society, 2017.Description: v, 108 pages ; 26 cmISBN:
  • 9781470422608 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Analysis and geometry on quasi-metric spaces -- 3. T(1) and local T(b) theorems for square functions -- 4. An inductive scheme for square function estimates -- 5. Square function estimates on uniformly rectifiable sets -- 6. Lp square function estimates -- 7. Conclusion.
Summary: 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.
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"Volume 245, number 1159 (fourth of 6 numbers), January 2017."

Includes bibliographical references (pages 105-108).

1. Introduction --
2. Analysis and geometry on quasi-metric spaces --
3. T(1) and local T(b) theorems for square functions --
4. An inductive scheme for square function estimates --
5. Square function estimates on uniformly rectifiable sets --
6. Lp square function estimates --
7. Conclusion.

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.

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