L^p-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (Memoirs of the American Mathematical Society) - Softcover

Steve Hofmann; Dorina Mitrea; Marius Mitrea; Andrew J. Morris

 
9781470422608: L^p-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 1470422603 ISBN 13: 9781470422608
Publisher: American Mathematical Society, 2017

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

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.

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2017
Language
English
ISBN 10 
1470422603
ISBN 13 
9781470422608
Binding
Paperback
Number of pages
108