On the embedding of into
Author:
Guillermo Rey
Journal:
Proc. Amer. Math. Soc. 144 (2016), 4455-4470
MSC (2010):
Primary 42B35; Secondary 46E30
DOI:
https://doi.org/10.1090/proc/13087
Published electronically:
April 25, 2016
MathSciNet review:
3531194
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We give a quantitative embedding of the Muckenhoupt class into
. In particular, we show how
depends on
in the inequality which characterizes
weights:




- [1] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, https://doi.org/10.4064/sm-51-3-241-250
- [2]
C. Domingo-Salazar, M. T. Lacey, and G. Rey, Borderline weak-type estimates for singular integrals and square functions,
Bulletin of the London Mathematical Society, Dec. 2015. - [3] Tuomas Hytönen, Carlos Pérez, and Ezequiel Rela, Sharp reverse Hölder property for 𝐴_{∞} weights on spaces of homogeneous type, J. Funct. Anal. 263 (2012), no. 12, 3883–3899. MR 2990061, https://doi.org/10.1016/j.jfa.2012.09.013
- [4] Antonios D. Melas, A sharp 𝐿^{𝑝} inequality for dyadic 𝐴₁ weights in ℝⁿ, Bull. London Math. Soc. 37 (2005), no. 6, 919–926. MR 2186725, https://doi.org/10.1112/S0024609305004765
- [5]
F. Nazarov, A. Reznikov, V. Vasyunin, and A. Volberg, A Bellman function counterexample to the
conjecture: The blow-up of the weak norm estimates of weighted singular operators,
ArXiv e-prints, June 2015. - [6] F. Nazarov, S. Treil, and A. Volberg, The Bellman functions and two-weight inequalities for Haar multipliers, J. Amer. Math. Soc. 12 (1999), no. 4, 909–928. MR 1685781, https://doi.org/10.1090/S0894-0347-99-00310-0
- [7] Adam Osȩkowski, Sharp inequalities for dyadic 𝐴₁ weights, Arch. Math. (Basel) 101 (2013), no. 2, 181–190. MR 3089774, https://doi.org/10.1007/s00013-013-0537-9
- [8] Guillermo Rey and Alexander Reznikov, Extremizers and sharp weak-type estimates for positive dyadic shifts, Adv. Math. 254 (2014), 664–681. MR 3161110, https://doi.org/10.1016/j.aim.2013.12.030
- [9] Leonid Slavin, Alexander Stokolos, and Vasily Vasyunin, Monge-Ampère equations and Bellman functions: the dyadic maximal operator, C. R. Math. Acad. Sci. Paris 346 (2008), no. 9-10, 585–588 (English, with English and French summaries). MR 2412802, https://doi.org/10.1016/j.crma.2008.03.003
- [10] V. I. Vasyunin, The exact constant in the inverse Hölder inequality for Muckenhoupt weights, Algebra i Analiz 15 (2003), no. 1, 73–117 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 15 (2004), no. 1, 49–79. MR 1979718, https://doi.org/10.1090/S1061-0022-03-00802-1
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B35, 46E30
Retrieve articles in all journals with MSC (2010): 42B35, 46E30
Additional Information
Guillermo Rey
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email:
reyguill@math.msu.edu
DOI:
https://doi.org/10.1090/proc/13087
Received by editor(s):
April 27, 2015
Received by editor(s) in revised form:
January 2, 2016
Published electronically:
April 25, 2016
Communicated by:
Svitlana Mayboroda
Article copyright:
© Copyright 2016
American Mathematical Society