Extra cancellation of even Calderón-Zygmund operators and quasiconformal mappings

Journal des Mathematiques Pures et Appliquees

Volumn 91, Issue 4, 2009, Pages 402-431

  Mateu, Joan ^a   Orobitg, Joan ^a   Verdera, Joan ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Beltrami equations; Calder n Zygmund kernels; Quasiconformal mappings

Indexed keywords

EID: 63449122818     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2009.01.010     Document Type: Article

References (26)

1. Ahlfors L. Lectures on Quasiconformal Mappings. University Lecture Series. second ed. vol. 38 (2006), American Mathematical Society, Providence, RI
2. Astala K. Area distortion of quasiconformal mappings. Acta Math. 173 (1994) 37-60
3. Astala K., Clop A., Mateu J., Orobitg J., and Uriarte-Tuero I. Distortion of Hausdorff measures and improved Painlevé removability for quasiregular mappings. Duke Math. J. 141 3 (2008) 539-571
4. Astala K., Iwaniec T., and Martin G. Elliptic Equations and Quasiconformal Mappings in the Plane. Princeton Mathematical Series vol. 47 (2009), Princeton University Press
5. Astala K., Iwaniec T., and Saksman E. Beltrami operators in the plane. Duke Math. J. 107 (2001) 27-56
6. 1, p. Publ. Mat. 53 (2009) 197-230
7. 1, 2-Beltrami coefficients. Math. Res. Lett. 15 4 (2008) 779-793
8. Depauw N. Poche de tourbillon pour Euler 2D dans un ouvert à bord. J. Math. Pures Appl. 78 3 (1999) 313-351
9. García-Cuerva J.L., and Gatto A.E. Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures. Publ. Mat. 49 (2005) 285-296
10. Gatto A.E. On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces. Collect. Math. 60 (2009) 101-114
11. p-Theory of Quasiregular Mappings. Lecture Notes in Math. vol. 1508 (1992), Springer, Berlin
12. Iwaniec T. The best constant in a BMO-inequality for the Beurling-Ahlfors transform. Mich. Math. J. 34 (1987) 407-434
13. Johnson J.A. Banach spaces of Lipschitz functions and vector-valued Lipschitz functions. Trans. Amer. Math. Soc. 148 (1970) 147-169
14. Lacey M.T., Sawyer E.T., and Uriarte-Tuero I. Astala's conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane. arXiv:0805.4711
15. Lehto O., and Virtanen K.I. Quasiconformal Mappings in the Plane. second ed. (1973), Springer-Verlag, New York
16. Li Y.Y., and Nirenberg L. Estimates for elliptic systems from composite material. Comm. Pure Appl. Math. 56 7 (2003) 892-925
17. Li Y.Y., and Vogelius M.S. Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Rational Mech. Anal. 153 2 (2000) 91-151
18. Morrey C.B. On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43 1 (1938) 126-166
19. Mateu J., Orobitg J., and Verdera J. Estimates for the maximal singular integral in terms of the singular integral: The case of even kernels. arXiv:0707.4610v1
20. 1 estimates for the maximal Riesz transform and the maximal Beurling transform. Math. Res. Lett. 13 5-6 (2006) 957-966
21. Rohde S. Bi-Lipschitz maps and the modulus of rings. Ann. Acad. Sci. Fenn. Math. 22 2 (1997) 465-474
22. Schechter M. Principles of Functional Analysis. student ed. (1973), Academic Press/Harcourt Brace Jovanovich Publishers, New York/London
23. Stein E.M. Singular Integrals and Differentiability Properties of Functions (1970), Princeton University Press, Princeton
24. Tolsa X. Bilipschitz maps, analytic capacity, and the Cauchy integral. Ann. of Math. 162 (2005) 1243-1304
25. 2 boundedness of the Cauchy integral and Menger curvature. Contemp. Math. 277 (2001) 139-158
26. Wittmann R. Application of a theorem of M.G. Krein to singular integrals. Trans. Amer. Math. Soc. 299 2 (1987) 581-599