Variation for singular integrals on Lipschitz graphs: and endpoint estimates
Author:
Albert Mas
Journal:
Trans. Amer. Math. Soc. 365 (2013), 57595781
MSC (2010):
Primary 42B20, 42B25
Published electronically:
June 6, 2013
MathSciNet review:
3091264
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Abstract: Let be integers and let denote the dimensional Hausdorff measure restricted to an dimensional Lipschitz graph in with slope strictly less than . For , we prove that the variation and oscillation for CalderónZygmund singular integrals with odd kernel are bounded operators in for , from to , and from to . Concerning the first endpoint estimate, we actually show that such operators are bounded from the space of finite complex Radon measures in to .
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Additional Information
Albert Mas
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain
Email:
amasblesa@gmail.com
DOI:
http://dx.doi.org/10.1090/S000299472013058151
Keywords:
$\rho$variation and oscillation,
Calder\'onZygmund singular integrals.
Received by editor(s):
September 22, 2011
Published electronically:
June 6, 2013
Additional Notes:
The author was partially supported by grants AP200602416 (FPU program, Spain), MTM201016232 (Spain), and 2009SGR000420 (Generalitat de Catalunya, Spain).
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
