Continuity of weighted estimates in $A_{p}$ norm
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- by Nikolaos Pattakos and Alexander Volberg PDF
- Proc. Amer. Math. Soc. 140 (2012), 2783-2790 Request permission
Abstract:
We prove that for a general CalderĂłn-Zygmund operator $T$ the numbers $\|T\|_{L^{p}(w)\rightarrow L^{p}(w)}$ converge to $\|T\|_{L^{p}(dx)\rightarrow L^{p}(dx)}$ as the $A_{p}$ norm of $w$ converges to $1$, i.e. as $[w]_{A_{p}}\rightarrow 1^{+}$ for $1<p<\infty$.References
- JosĂ© GarcĂa-Cuerva and JosĂ© L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de MatemĂĄtica [Mathematical Notes], 104. MR 807149
- Stefan Geiss, Stephen Montgomery-Smith, and Eero Saksman, On singular integral and martingale transforms, Trans. Amer. Math. Soc. 362 (2010), no. 2, 553â575. MR 2551497, DOI 10.1090/S0002-9947-09-04953-8
- T. Hytönen, C. Pérez, S. Treil, and A. Volberg, Sharp weighted estimates of the dyadic shifts and $A_2$ conjecture. arXiv:1010.0755 2010.
- Michael Brian Korey, Correction to: âOptimal factorization of Muckenhoupt weightsâ [Trans. Amer. Math. Soc. 352 (2000), no. 11, 5251â5262; MR1694375 (2001b:42023)], Trans. Amer. Math. Soc. 353 (2001), no. 2, 839â851. MR 1806041, DOI 10.1090/S0002-9947-00-02789-6
- Michael Brian Korey, Ideal weights: asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation, J. Fourier Anal. Appl. 4 (1998), no. 4-5, 491â519. MR 1658636, DOI 10.1007/BF02498222
- E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159â172. MR 92943, DOI 10.1090/S0002-9947-1958-0092943-6
- S. Treil and A. Volberg, Completely regular multivariate stationary processes and the Muckenhoupt condition, Pacific J. Math. 190 (1999), no. 2, 361â382. MR 1722900, DOI 10.2140/pjm.1999.190.361
Additional Information
- Nikolaos Pattakos
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 960560
- Email: pattakos@msu.edu
- Alexander Volberg
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Received by editor(s): December 1, 2010
- Received by editor(s) in revised form: March 7, 2011
- Published electronically: December 13, 2011
- Communicated by: Mario Bonk
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 2783-2790
- MSC (2010): Primary 30E20, 47B37, 47B40, 30D55
- DOI: https://doi.org/10.1090/S0002-9939-2011-11165-1
- MathSciNet review: 2910765