$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets
- ISBN-10
- 1470422603
- ISBN-13
- 9781470422608
- Category
- Function spaces
- Pages
- 108
- Language
- English
- Published
- 2017-01-18
- Publisher
- American Mathematical Soc.
- Authors
- Steve Hofmann, Dorina Mitrea, Marius Mitrea
Description
The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local 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 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 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.
Get the book
Similar books
-
Multi-Layer Potentials and Boundary Problems: for Higher-Order Elliptic Systems in Lipschitz Domains
By Marius Mitrea, Irina MitreaJ. 46, 27–42 (1979) P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, vol. ... A.J. Morris, Lp-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets, ...
-
Selected Papers on Analysis and Differential Equations
By American Mathematical SocietyMR0131498 (24:A1348) P. W. Jones, Square functions, Cauchy integrals, analytic capacity, and harmonic measure, In: Harmonic ... MR2010347 (2004m:42021) R. A. Mac ́ıas and C. Segovia, Lipschitz functions on spaces of homogeneous type, ...
-
Lectures on Singular Integral Operators
By Francis Michael Christ[JPI] P. W. Jones, Square functions, Cauchy inzegrals, analytic capacity and harmonic measure, Harmonic Analysis and Partial ... [MS] R. Macias and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math.
-
Mathematical Reviews
By Andoni Ibarra, Thomas MormannMathematical Reviews
-
Elliptic Theory for Sets with Higher Co-Dimensional Boundaries
By Guy David, Joseph Feneuil, Svitlana MayborodaView the abstract.
-
Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems
By Carlos E. KenigKenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form.
-
Harmonic Analysis on Spaces of Homogeneous Type
By Donggao Deng, Yongsheng HanThis book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set?
-
Index of Mathematical Papers
Index of Mathematical Papers
-
Fractals in Probability and Analysis
By Christopher J. Bishop, Yuval PeresA mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
-
Classical Fourier Analysis
By Loukas GrafakosThe primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject.