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

Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew J. Morris (Autoren)

Buch | Softcover

108 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-2260-8 (ISBN)

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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.

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.

Introduction
Analysis and geometry on quasi-metric spaces
$T(1)$ and local $T(b)$ theorems for square functions
An inductive scheme for square function Estimates
Square function estimates on uniformly rectifiable sets
$L^p$ square function estimates
Conclusion
References.

Erscheinungsdatum	31.01.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	185 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2260-3 / 1470422603
ISBN-13	978-1-4704-2260-8 / 9781470422608
Zustand	Neuware