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

Format:

Book

Author/Creator:

Hofmann, Steve, 1958- author.

Series:

Memoirs of the American Mathematical Society ; Volume 245, Number 1159 (fourth of 6 numbers)

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 245, Number 1159 (fourth of 6 numbers)

Language:

English

Subjects (All):

Homogeneous spaces.

Lie groups.

Function spaces.

Geometric measure theory.

Physical Description:

1 online resource (120 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

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. 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.

Contents:

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

Lp square function estimates.

Notes:

Includes bibliographical references.

Description based on print version record.

"Volume 245, number 1159 (fourth of 6 numbers), January 2017."

ISBN:

1-4704-3607-8